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Algebraic K-theory

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Abstract

One gives a survey of the fundamental methods and results of the algebraic K-theory obtained in the past decade. One presents the basic constructions of the K-theory of rings and of the K-theory of exact categories. A special attention is given to the K-theory of schemes.

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Literature cited

  1. A. A. Beilinson, “Higher regulators and values of L-functions of curves,” Funkts. Anal. Prilozhen.,14, No. 2, 46–47 (1980).

    Google Scholar 

  2. L. N. Vasershtein, “K1-theory and the congruence problem,” Mat. Zametki,5, No. 2, 233–244 (1968).

    Google Scholar 

  3. L. N. Vasershtein, “On the stabilization of the general linear group over a ring,” Mat. Sb.,79, No. 3, 405–424 (1969).

    Google Scholar 

  4. L. N. Vasershtein, “The stabilization of unitary and orthogonal groups over a ring with involution,” Mat. Sb.,81, No. 3, 328–351 (1970).

    Google Scholar 

  5. L. N. Vasershtein, “The stable range of rings and the dimension of topological spaces,” Funkts. Anal. Prilozhen.,5, No. 2, 17–27 (1971).

    Google Scholar 

  6. L. N. Vasershtein, “On the SL2 group over Dedekind rings of arithmetic type,” Mat. Sb.,89, No. 2, 313–322 (1972).

    Google Scholar 

  7. L. N. Vasershtein, “The structure of the classical arithmetic groups of rank greater than one,” Mat. Sb.,91, No. 3, 445–470 (1973).

    Google Scholar 

  8. L. N. Vasershtein, “The stabilization for classical groups over rings,” Mat. Sb.,93, No. 2, 268–295 (1974).

    Google Scholar 

  9. L. N. Vasershtein, “On the stabilization for Milnor's K2 functor,” Usp. Mat. Nauk,30, No. 1, 224 (1975).

    Google Scholar 

  10. L. N. Vasershtein, “The foundations of algebraic K-theory,” Usp. Mat. Nauk,31, No. 4, 87–149 (1976).

    Google Scholar 

  11. L. N. Vasershtein and A. V. Mikhalev, “On the normal subgroups of the orthogonal group over a ring with involution,” Algebra Logika,9, No. 6, 629–632 (1970).

    Google Scholar 

  12. L. N. Vasershtein and A. A. Suslin, “On Serre's problem on projective modules over polynomial rings, and algebraic K-theory,” Izv. Akad. Nauk SSSR, Ser. Mat.,40, No. 5, 993–1054 (1976).

    Google Scholar 

  13. I. A. Volodin, “Algebraic K-theory as an extraordinary homology theory on the category of associative rings with identity,” Izv. Akad. Nauk SSSR, Ser. Mat.,35, No. 4, 844–873 (1971).

    Google Scholar 

  14. I. A. Volodin, “Algebraic K-theory,” Usp. Mat. Nauk,27, No. 4, 207–208 (1972).

    Google Scholar 

  15. I. A. Volodin, “Generalized Whitehead groups and pseudoisotopies,” Usp. Mat. Nauk,27, No. 5, 229–230 (1972).

    Google Scholar 

  16. V. E. Voskresenskii, “On the reduced Whitehead group of a simple algebra,” Usp. Mat. Nauk,32, No. 6, 247–248 (1977).

    Google Scholar 

  17. I. Golubchik, “On the general linear group over an associative ring,” Usp. Mat. Nauk,28, No. 3, 179–180 (1973).

    Google Scholar 

  18. Kh. N. Inasaridze, “Homotopy of pseudosimplicial groups and non-Abelian derived functors,” Soobshch. Akad. Nauk GSSR,76, No. 3, 533–536 (1974).

    Google Scholar 

  19. Kh. N. Inasaridze, Certain Questions of Homological and Homotopical Algebra and Their Applications [in Russian], Metsniereba, Tbilisi (1975).

    Google Scholar 

  20. Kh. N. Inasaridze, “Homotopy of pseudosimplicial groups, non-Abelian derived functors, and algebraic K-theory,” Mat. Sb.,98, No. 3, 339–362 (1975).

    Google Scholar 

  21. Kh. N. Inasaridze, “On algebraic K-functors,” Soobshch. Akad. Nauk GSSR,77, 17–20 (1975).

    Google Scholar 

  22. I. S. Klein and A. V. Mikhalev, “The orthogonal Steinberg group over a ring with involution,” Algebra Logika,9, No. 2, 145–166 (1970).

    Google Scholar 

  23. I. S. Klein and A. V. Mikhalev, “The unitary Steinberg group over a ring with involution,” Algebra Logika,9, No. 5, 510–519 (1970).

    Google Scholar 

  24. V. I. Kopeiko, “Quadratic spaces and quaterion algebras,” Zap. Nauch. Sem. LOMI,75, 110–120 (1978).

    Google Scholar 

  25. V. I. Kopeiko, “The stabilization of symplectic groups over a polynomial ring,” Mat. Sb.,106, No. 1, 94–107 (1978).

    Google Scholar 

  26. V. I. Kopeiko and A. A. Suslin, “On quadratic modules over polynomial rings,” J. Sov. Math.,17, No. 4 (1981).

  27. Yu. I. Manin, “Lectures on the K-functor in algebraic geometry,” Usp. Mat. Nauk,24, No. 5, 3–86 (1969).

    Google Scholar 

  28. A. S. Merkur'ev, “On the norm residue symbol of degree 2,” Dokl. Akad. Nauk SSSR,261, No. 3, 542–547 (1981).

    Google Scholar 

  29. A. S. Merkur'ev and A. A. Suslin, “On the homomorphism of the norm residue,” Preprint LOMI (1982).

  30. N. M. Mustafa-zade, “The invariance of higher K-functors on classes of Clifford algebras,” Usp. Mat. Nauk,29, No. 3, 215–216 (1974).

    Google Scholar 

  31. N. M. Mustafa-zade, “On epimorphic stability of the unitary K2-functor,” Usp. Mat. Nauk,35, No. 6, 165–166 (1980).

    Google Scholar 

  32. S. P. Novikov, “Algebraic construction and properties of Hermitian analogues of K-theory over rings with involution from the viewpoint of the Hamiltonian formalism. Certain applications to differential topology and the theory of characteristic classes. I, II,” Izv. Akad. Nauk SSSR, Ser. Mat.,34, No. 2, 253–288 (1970);34, No. 3, 475–500 (1970).

    Google Scholar 

  33. A. N. Parshin, “Class fields and algebraic K-theory,” Usp. Mat. Nauk,30, No. 1, 253–254 (1975).

    Google Scholar 

  34. A. N. Parshin, “Abelian coverings of arithmetic schemes,” Dokl. Akad. Nauk SSSR,243, No. 4, 855–858 (1978).

    Google Scholar 

  35. T. I. Pirashvili, “On satellites and non-Abelian derived functors,” Soobshch. Akad. Nauk GSSR,87, No. 3, 533–536 (1977).

    Google Scholar 

  36. T. I. Pirashvili, “On non-Abelian derived functors,” Tr. Tbilis. Mat. Inst. Akad. Nauk GSSR,62, 91–104 (1979).

    Google Scholar 

  37. T. I. Pirashvili, “Algebraic Karoubi-Villamayor and Bass functors for ringoids,” Soobshch. Akad. Nauk GSSR,92, No. 3, 573–576 (1978).

    Google Scholar 

  38. V. P. Platonov, “The Tannaka-Artin problem and groups of projective conorms,” Dokl. Akad. Nauk SSSR,222, No. 6, 1299–1302 (1975).

    Google Scholar 

  39. V. P. Platonov, “On the Tannaka-Artin problem,” Dokl. Akad. Nauk SSSR,221, No. 5, 1038–1041 (1975).

    Google Scholar 

  40. V. P. Platonov, “The Tannaka-Artin problem and reduced K-theory,” Izv. Akad. Nauk SSSR, Ser. Mat.,40, No. 2, 227–261 (1976).

    Google Scholar 

  41. V. P. Platonov, “The reduced Whitehead group for cyclic algebras,” Dokl. Akad. Nauk SSSR,228, No. 1, 38–40 (1976).

    Google Scholar 

  42. V. P. Platonov, “On the infiniteness of the reduced Whitehead group,” Dokl. Akad. Nauk SSSR,227, No. 2, 299–301 (1976).

    Google Scholar 

  43. V. P. Platonov, “On reduced K-theory for n-fold Henselian fields,” Dokl. Akad. Nauk SSSR,249, No. 6, 1318–1320 (1979).

    Google Scholar 

  44. V. P. Platonov and V. I. Yanchevskii, “SK1 for division rings of noncommutative rational functions,” Dokl. Akad. Nauk SSSR,249, No. 5, 1064–1068 (1979).

    Google Scholar 

  45. A. V. Prasolov, “Preadditive categories and K-theory,” Usp. Mat. Nauk,32, No. 5, 195–196 (1977).

    Google Scholar 

  46. Sh. Sakalosh, “On projective functors on free categories,” Mat. Sb.,114, No. 3, 425–437 (1981).

    Google Scholar 

  47. Yu. P. Solov'ev, “Quillen's construction in the Hermitian K-theory,” Dokl. Akad. Nauk SSSR,253, No. 2, 301–304 (1980).

    Google Scholar 

  48. A. A. Suslin, “On projective modules over polynomial rings,” Mat. Sb.,93, No. 4, 588–595 (1974).

    Google Scholar 

  49. A. A. Suslin, “Projective modules over polynomial rings are free,” Dokl. Akad. Nauk SSSR,229, No. 5, 1063–1066 (1976).

    Google Scholar 

  50. A. A. Suslin, “On a theorem of Cohn,” J. Sov. Math.,17, No. 2 (1981).

  51. A. A. Suslin, “A cancellation theorem for projective modules over algebras,” Dokl. Akad. Nauk SSSR,236, No. 4, 808–811 (1977).

    Google Scholar 

  52. A. A. Suslin, “On the structure of the special linear group over polynomial rings,” Izv. Akad. Nauk SSSR, Ser. Mat.,41, No. 2, 235–252 (1977).

    Google Scholar 

  53. A. A. Suslin, “On stably free modules,” Mat. Sb.,102, No. 4, 537–550 (1977).

    Google Scholar 

  54. A. A. Suslin, “The cancellation problem for projective modules,” Preprint LOMI, P-4-77.

  55. A. A. Suslin, “Locally polynomial rings and symmetric algebras,” Izv. Akad. Nauk SSSR, Ser. Mat.,41, No. 3, 503–515 (1977).

    Google Scholar 

  56. A. A. Suslin, “On the structure of projective modules over polynomial rings in the case of a noncommutative ring of coefficients,” Tr. Mat. Inst. Akad. Nauk SSSR,148, 233–252 (1978).

    Google Scholar 

  57. A. A. Suslin, “Reciprocity laws and the stable range of polynomial rings,” Izv. Akad. Nauk SSSR, Ser. Mat.,43, No. 6, 1394–1429 (1979).

    Google Scholar 

  58. A. A. Suslin, “The cancellation problem for projective modules and related questions,” in: Proc. Int. Congress Math. (Helsinki 1978), Vol. 1 (1980), pp. 160–164.

    Google Scholar 

  59. A. A. Suslin and V. I. Kopeiko, “Quadratic modules and the orthogonal group over polynomial rings,” J. Sov. Math.,20, No. 6 (1982).

  60. A. A. Suslin and M. S. Tulenbaev, “A theorem on stabilization for Milnor's K2-functor,” J. Sov. Math.,17, No. 2 (1981).

  61. M. S. Tulenbaev, “The Schur multiplier of the group of elementary matrices of finite order,” J. Sov. Math.,17, No. 4 (1981).

  62. D. R. Farjas and R. L. Snider, “Ko and Noetherian group rings,” J. Algebra,42, No. 1, 192–198 (1976).

    Google Scholar 

  63. A. F. Kharshiladze, “Hermitian K-theory and quadratic extensions of rings,” Tr. Mosk. Mat. Obshch.,41, 3–36 (1980).

    Google Scholar 

  64. V. V. Shekhtman, “Algebraic K-theory and characteristic classes,” Usp. Mat. Nauk,33, No. 6, 239–240 (1978).

    Google Scholar 

  65. V. V. Shekhtman, “The Riemann-Roch theorem in algebraic K-theory,” Moscow State Univ. (1979). (Manuscript deposited at VINITI, July 3, 1979, No. 2425-79 Dep.)

  66. V. V. Shekhtman, “The Riemann-Roch theorem and the Atiyah-Hirzebruch spectral sequence,” Usp. Mat. Nauk,35, No. 6, 179–180 (1980).

    Google Scholar 

  67. V. I. Yanchevskii, “Division algebras over Henselian discretely valued fields and the Tannaka-Artin problem,” Dokl. Akad. Nauk SSSR,226, No. 2, 281–283 (1976).

    Google Scholar 

  68. V. I. Yanchevskii, “Reduced unitary Whitehead groups of skew-fields of noncommutative rational functions,” J. Sov. Math.,19, No. 1 (1982).

  69. V. I. Yanchevskii, “Reduced unitary Whitehead groups and noncommutative rational functions,” Dokl. Akad. Nauk BSSR,24, No. 7, 588–591 (1980).

    Google Scholar 

  70. V. I. Yanchevskii, “Commutants of simple algebras with a surjective reduced norm,” Dokl. Akad. Nauk SSSR,221, No. 5, 1056–1058 (1975).

    Google Scholar 

  71. R. M. F. Moss and C. B. Thomas (eds.), Algebraic K-Theory and Its Geometric Applications, Springer-Verlag, Berlin (1969).

    Google Scholar 

  72. G. Almkvist, “K-theory of endomorphisms,” J. Algebra,55, No. 2, 308–340 (1978).

    Google Scholar 

  73. R. Alperin, “Homology of SL2 (Z[ω]),” Comment. Math. Helv.,55, No. 3, 364–377 (1980).

    Google Scholar 

  74. R. Alperin, “SL2(Z[(1+√5)/2]),” Duke Math. J.,47, No. 3, 487–509 (1980).

    Google Scholar 

  75. R. Alperin, “Stability for H2(SUn),” Lect. Notes Math.,551, 283–289 (1976).

    Google Scholar 

  76. R. Alperin and R. K. Dennis, “K2 of quaternion algebras,” J. Algebra,56, No. 1, 262–273 (1979).

    Google Scholar 

  77. R. Alperin, R. K. Dennis, and M. R. Stein, “The nontriviality of SK1(Zπ),” Lect. Notes Math.,253, 1–7 (1973).

    Google Scholar 

  78. R. Alperin, and D. Wright, “K2(2, k[T, T−1]) is generated by ‘Symbols,’” J. Algebra,59, No. 1, 39–46 (1979).

    Google Scholar 

  79. S. A. Amitsur, L. H. Rowen, and J. P. Tignol, “Division algebras of degree 4 and 8 with involution,” Israel J. Math.,33, No. 2, 133–148 (1979).

    Google Scholar 

  80. D. F. Anderson, “Projective modules over subrings of k[X, Y] generated by monomials,” Pac. J. Math.,79, No. 1, 5–17 (1978).

    Google Scholar 

  81. D. F. Anderson, “Projective modules over subrings of k[X, Y],” Trans. Am. Math. Soc.,240, 317–328 (1978).

    Google Scholar 

  82. D. W. Anderson, “Relationship among K-theories,” Lect. Notes Math.,341, 57–72 (1973).

    Google Scholar 

  83. D. W. Anderson, “K-theory, simplicial complexes and categories,” in: Actes du Congres Internat. Math. (Nice, 1970), Tome 2, Gauthier-Villars, Paris (1971), pp. 3–11.

    Google Scholar 

  84. D. W. Anderson, M. Karoubi, and J. Wagoner, “Relations between higher algebraic K-theories,” Lect. Notes Math.,341, 73–81 (1973).

    Google Scholar 

  85. D. Anderson, M. Karoubi, and J. Wagoner, “Higher algebraic K-theories,” Trans. Am. Math. Soc.,226, 209–225 (1977).

    Google Scholar 

  86. G. A. Anderson, “Relative K-theory and surgery of n-ads,” Yokohama Math. J.,25, No. 2, 101–107 (1977).

    Google Scholar 

  87. D. M. Arnold, “Grothendieck and Whitehead groups of torsion free abelian groups,” Bull. Am. Math. Soc.,79, No. 4, 723–724 (1973).

    Google Scholar 

  88. D. M. Arnold, “On the algebraic K-theory of torsion free Abelian groups of finite rank,” in: Symp. Math., Vol. XIII (Convegno di Gruppi Abeliani, INDAM, Rome, 1972), Academic Press, London (1974), pp. 179–193.

    Google Scholar 

  89. A. Ash, “Cohomology of subgroups of finite index of SL(3,Z) and SL(4,Z),” Bull. Am. Math. Soc.,83, No. 3, 367–368 (1977).

    Google Scholar 

  90. A. Ash, “Cohomology of congruence subgroups of SL(n, Z),” Math. Ann.,249, No. 1, 55–73 (1980).

    Google Scholar 

  91. A. Bak, “On modules with quadratic forms,” Lect. Notes Math.,108, 55–66 (1969).

    Google Scholar 

  92. A. Bak and U. Rehmann, “Le probleme des sous-groupes de congruence dans SLn⩾2 sur un corps gauche,” C. R. Acad. Sci. Paris,AB289, No. 3, A151 (1979).

    Google Scholar 

  93. F. W. Barnes, “On the 2-torsion in the K2 of fields,” Math. Ann.,220, No. 1, 25–36 (1976).

    Google Scholar 

  94. H. Bass, “Algebraic K-theory: a historical survey,” in: Proc. Int. Congress of Math. (Vancouver, 1974), Vol. 1, Can. Math. Congress, Montreal (1975), pp. 277–283.

  95. H. Bass, “Ranks of projective ZG-modules,” Queen's Papers in Pure and Appl. Math., No. 42, 62–69 (1975).

    Google Scholar 

  96. H. Bass, “Liberation des modules projectifs sur certains anneaux de polynômes,” Lect. Notes Math.,431, 228–254 (1975).

    Google Scholar 

  97. H. Bass, “Is SK1(Zπ)=0 for π a finite Abelian group?,” Lect. Notes Math.,353, 84 (1973).

    Google Scholar 

  98. H. Bass, “Some problems in ‘classical’ algebraic K-theory,” Lect. Notes Math.,342, 3–73 (1973).

    Google Scholar 

  99. H. Bass, “L3 of finite abelian groups,” Ann. Math.,99, No. 1, 118–153 (1974).

    Google Scholar 

  100. H. Bass, “K2 des corps globaux (d'apres J. Tate, H. Garland, …),” Lect. Notes Math.,244, 233–255 (1971).

    Google Scholar 

  101. H. Bass, “Modules which support nonsingular forms,” J. Algebra,13, No. 2, 246–252 (1969).

    Google Scholar 

  102. H. Bass, “K2 and symbols,” Lect. Notes Math.,108, 1–11 (1969).

    Google Scholar 

  103. H. Bass, Algebraic K-Theory, Benjamin, New York (1968).

    Google Scholar 

  104. H. Bass, “K-theory and stable algebra,” Inst. Hautes Études Sci. Publ. Math., No. 22, 5–60 (1964).

    Google Scholar 

  105. H. Bass, “The Dirichlet unit theorem, induced characters, and Whitehead groups of finite groups,” Topology,4, No. 4, 391–410 (1966).

    Google Scholar 

  106. H. Bass, “Projective modules over free groups are free,” J. Algebra,1, No. 4, 367–373 (1964).

    Google Scholar 

  107. H. Bass, E. H. Connell, and D. L. Wright, “Local polynomial algebras are symmetric,” Bull. Am. Math. Soc.,82, No. 5, 719–720 (1976).

    Google Scholar 

  108. H. Bass, A. Heller, and R. G. Swan, “The Whitehead group of a polynomial extension,” Inst. Hautes Études Sci. Publ. Math., No. 22, 545–563 (1964).

    Google Scholar 

  109. H. Bass, J. Milnor, and J.-P. Serre, “Solution of the congruence subgroup problem for SLn (n⩾3) and Sp2n (n⩾2),” Inst. Hautes Études Sci. Publ. Math., No. 33, 59–137 (1967).

    Google Scholar 

  110. H. Bass and J. Tate, “The Milnor ring of a global field,” Lect. Notes Math.,342, 349–446 (1973).

    Google Scholar 

  111. P. Baum, W. Fulton, and R. MacPherson, “Riemann-Roch and topological K-theory for singular varieties,” Acta Math.,143, Nos. 3–4, 155–192 (1979).

    Google Scholar 

  112. P. Baum, W. Fulton, and G. Quart, “Lefschetz-Riemann-Roch for singular varieties,” Acta Math.,143, Nos. 3–4, 193–211 (1979).

    Google Scholar 

  113. Gr. W. Bell, “On the cohomology of the finite special linear groups. I,” J. Algebra,54, No. 1, 216–238 (1978).

    Google Scholar 

  114. Gr. W. Bell, “On the cohomology of the finite special linear groups. II,” J. Algebra,54, 239–259 (1978).

    Google Scholar 

  115. P. H. Berridge and M. J. Dunwoody, “Non-free projective modules for torsion-free groups,” J. London Math. Soc.,19, No. 3, 433–436 (1979).

    Google Scholar 

  116. B. J. Birch, “K2 of global fields,” Proc. Symp. Pure Math.,20 (1970).

  117. S. Bloch, “Torsion algebraic cycles and a theorem of Roitman,” Compositio Math.,39, No. 1, 107–127 (1979).

    Google Scholar 

  118. S. Bloch, “Some formulas pertaining to the K-theory of commutative groupschemes,” J. Algebra,53, No. 2, 304–326 (1978).

    Google Scholar 

  119. S. Bloch, “K2 of Artinian Q-algebras, with application to algebraic cycles,” Commun. Algebra,3, No. 5, 405–428 (1975).

    Google Scholar 

  120. S. Bloch, “Torsion algebraic cycles, K2 and Brauer groups of function fields,” Bull. Am. Math. Soc.,80, No. 5, 941–945 (1974).

    Google Scholar 

  121. S. Bloch, “Torsion algebraic cycles, K2, and Brauer groups of function fields,” Lect. Notes Math.,844, 75–102 (1981).

    Google Scholar 

  122. S. Bloch, “On the tangent space to Quillen K-theory,” Lect. Notes Math.,341, 205–210 (1973).

    Google Scholar 

  123. S. Bloch, “Algebraic K-theory and algebraic geometry,” Lect. Notes Math.,341, 259–265 (1973).

    Google Scholar 

  124. S. Bloch, “K2 and algebraic cycles,” Ann. Math.,99, No. 2, 349–379 (1974).

    Google Scholar 

  125. S. Bloch, “Algebraic K-theory and crystalline cohomology,” Inst. Hautes Etudes Sci. Publ. Math.,47, 187–268 (1977).

    Google Scholar 

  126. S. Bloch, “Applications of the dilogarithm function in algebraic K-theory and algebraic geometry,” in: Proc. Internat. Symp. of Algebraic Geometry, Kyoto (1977), pp. 103–114.

  127. S. Bloch, “An example in the theory of algebraic cycles,” Lect. Notes Math.,551, 1–29 (1976).

    Google Scholar 

  128. S. Bloch, “The dilogarithm and extensions of Lie algebras,” Lect. Notes Math.,854, 1–23 (1981).

    Google Scholar 

  129. S. Bloch, “On the Chow groups of certain rational surfaces,” Ann. Sci. Ecole Norm. Sup.,14, No. 1, 41–59 (1981).

    Google Scholar 

  130. S. Bloch, “Algebraic K-theory and classifield theory for arithmetical surfaces,” Ann. Math.,114, No. 2, 229–265 (1981).

    Google Scholar 

  131. S. Bloch and J. P. Murre, “On the Chow group of certain types of Fano threefolds,” Compositio Math.,39, No. 1, 47–105 (1979).

    Google Scholar 

  132. S. Bloch and A. Ogus, “Gersten's conjecture and the homology of schemes,” Ann. Sci. Ecole Norm. Sup.,7, 181–201 (1974).

    Google Scholar 

  133. E. Bombieri, “Seminonnalità e singolarità ordinarie,” in: Symposia Mathematica, Vol. XI, Academic Press, London (1973), pp. 205–210.

    Google Scholar 

  134. M. Boratyński, “On a conjecture of M. P. Murthy,” Nagoya Math. J.,77, 41–45 (1980).

    Google Scholar 

  135. A. Borel, “Stable and L2-cohomology of arithmetic groups,” Bull. Am. Math. Soc. (N.S.),3, No. 3, 1025–1027 (1980).

    Google Scholar 

  136. A. Borel, “Cohomologie de SLn et valeurs de fonctions zeta aux points entiers,” Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4),4, No. 4, 613–636 (1977).

    Google Scholar 

  137. A. Borel, “Stable real cohomology of arithmetic groups,” Ann. Sci. Ecole Norm. Sup.,7, 235–272 (1974).

    Google Scholar 

  138. A. Borel and J.-P. Serre, “Le théorème de Riemann-Roch,” Bull. Soc. Math. France,86, No. 2, 97–136 (1958).

    Google Scholar 

  139. A. Borel and J.-P. Serre, “Corners and arithmetic groups,” Comment. Math. Helv.,48, No. 4, 436–491 (1973).

    Google Scholar 

  140. A. Borel and J.-P. Serre, “Cohomologie d'immeubles et de groupes S-arithmetiques,” Topology,15, No. 3, 211–232 (1976).

    Google Scholar 

  141. L. Breen, “Une théorème de finitude en K-théorie,” Lect. Notes Math.,431, 36–57 (1975).

    Google Scholar 

  142. J. W. Brewer and D. L. Costa, “Seminormality and projective modules over polynomial rings,” J. Algebra,58, No. 1, 208–216 (1979).

    Google Scholar 

  143. J. W. Brewer and D. L. Costa, “Projective modules over some non-Noetherian polynomial rings,” J. Pure Appl. Algebra,13, No. 2, 157–163 (1978).

    Google Scholar 

  144. J. W. Brewer, D. L. Costa, and K. McCrimmon, “Seminormality and root closure in polynomial rings and algebraic curves,” J. Algebra,58, No. 1, 217–226 (1979).

    Google Scholar 

  145. W. Browder, “Algebraic K-theory with coefficientsZ/p,” Lect. Notes Math.,657, 40–84 (1978).

    Google Scholar 

  146. K. S. Brown, “Cohomology of groups,” Lect. Notes Math.,551, 249–259 (1976).

    Google Scholar 

  147. K. S. Brown and S. M. Gersten, “Algebraic K-theory as generalized sheaf cohomology,” Lect. Notes Math.,341, 266–292 (1973).

    Google Scholar 

  148. R. Brown, “Quadratic forms with prescribed Stiefel-Whitney invariants,” Queen's Papers in Pure and Appl. Math., No. 46, 377–384 (1977).

    Google Scholar 

  149. I. Bucur, “Triangulated categories and algebraic K-theory,” Lect. Notes Math.,108, 28–54 (1969).

    Google Scholar 

  150. D. Burghelea, “Some rational computations of the Waldhausen algebraic K-theory,” Comment. Math. Helv.,54, No. 2, 185–198 (1979).

    Google Scholar 

  151. A. Candiotti, “Computations of Iwasawa invariants and K2,” Compositio Math.,29, No. 1, 89–111 (1974).

    Google Scholar 

  152. S. E. Cappell, “Unitary nilpotent groups and Hermitian K-theory. I,” Bull. Am. Math. Soc.,80, No. 6, 1117–1122 (1974).

    Google Scholar 

  153. J. E. Carroll, “On the torsion in K2 of local fields,” Lect. Notes Math.,342, 464–473 (1973).

    Google Scholar 

  154. D. W. Carter, “Lower K-theory of finite groups,” Commun. Algebra,8, No. 20, 1927–1937 (1980).

    Google Scholar 

  155. D. W. Carter, “Lower K-theory of nilpotent groups,” J. Algebra,66, No. 1, 134–146 (1980).

    Google Scholar 

  156. D. W. Carter, “Localization in lower algebraic K-theory,” Commun. Algebra,8, No. 7, 603–622 (1980).

    Google Scholar 

  157. A. J. Casson, “Whitehead groups of free products with amalgamation,” Lect. Notes Math.,342, 144–154 (1973).

    Google Scholar 

  158. R. M. Charney, “Homology stability for GLn of a Dedekind domain,” Invent. Math.,56, No. 1, 1–17 (1980).

    Google Scholar 

  159. S. U. Chase and W. C. Waterhouse, “Moore's theorem on uniqueness of reciprocity laws,” Invent. Math.,16, No. 3, 267–270 (1972).

    Google Scholar 

  160. K.-G. Choo, “Whitehead groups of semidirect products of free groups. II,” Glasgow Math. J.,21, No. 1, 71–74 (1980).

    Google Scholar 

  161. K.-G. Choo, “Whitehead groups of certain semidirect products of free groups,” Proc. Am. Math. Soc.,43, No. 1, 26–30 (1974).

    Google Scholar 

  162. K.-G. Choo, “Whitehead groups of twisted free associative algebras,” Pac. J. Math.,50, No. 2, 399–402 (1974).

    Google Scholar 

  163. K.-G. Choo, K. Y. Lam, and E. Luft, “On free product of rings and the coherence property,” Lect. Notes Math.,342, 135–143 (1973).

    Google Scholar 

  164. H. Bass (ed.), “Classical Algebraic K-Theory, and Connections with Arithmetic, Springer-Verlag, Berlin (1973).

    Google Scholar 

  165. F. J.-B. J. Clauwens, “The K-theory of almost-symmetric forms,” Math. Centre Tracts, No. 115, 41–49 (1979).

    Google Scholar 

  166. J. Coates, “K-theory and Iwasawa's analogue of the Jacobian,” Lect. Notes Math.,342, 502–520 (1973).

    Google Scholar 

  167. J. Coates, “Research problems: arithmetic questions in K-theory,” Lect. Notes Math.,342, 521–523 (1973).

    Google Scholar 

  168. J. Coates, “On K2 and some classical conjectures in algebraic number theory,” Ann. Math.,95, No. 1, 99–116 (1972).

    Google Scholar 

  169. P. M. Cohn, “On the structure of the GL2 of a ring,” Inst. Hautes Etudes Sci. Publ. Math., No. 30, 365–413 (1966).

    Google Scholar 

  170. E. H. Connell, “A K-theory for the category of projective algebras,” J. Pure Appl. Algebra,5, No. 3, 281–292 (1974).

    Google Scholar 

  171. E. H. Connell, “On the K-theory of algebras and polynomial extensions,” J. Pure Appl. Algebra,7, No. 2, 169–174 (1976).

    Google Scholar 

  172. E. H. Connell and M. K. Siu, “Localization in algebraic K-theory,” J. Algebra,30, Nos. 1–3, 37–41 (1974).

    Google Scholar 

  173. E. H. Connell and D. Wright, “A Mayer—Vietoris sequence in nonlinear K-theory,” J. Pure Appl. Algebra,16, No. 2, 149–165 (1980).

    Google Scholar 

  174. M. Cretin, “Invariance homotopique in K-théorie hermitienne,” Publ. Dép. Math. (Lyon),12, No. 1, 39–59 (1975).

    Google Scholar 

  175. M. Cretin, “L'espace classifiant de la K-théorie algebrique,” Publ. Dép. Math. (Lyon),12, No. 2, 57–69 (1975).

    Google Scholar 

  176. T. Cubota, “Topological coverings of SL2 over a local field,” J. Math. Soc. Jpn.,19, 114–121 (1967).

    Google Scholar 

  177. E. D. Davis, “On the geometric interpretation of seminormality,” Proc. Am. Math. Soc.,68, No. 1, 1–5 (1978).

    Google Scholar 

  178. B. H. Dayton, “K-theory of tetrahedra,” J. Algebra,56, No. 1, 129–144 (1979).

    Google Scholar 

  179. B. H. Dayton, “Homotopy and algebraic K-theory,” Pac. J. Math.,43, No. 2, 297–305 (1972).

    Google Scholar 

  180. B. H. Dayton, “SK1 of commutative normed algebras,” Lect. Notes Math.,551, 30–43 (1976).

    Google Scholar 

  181. B. H. Dayton, “Seminormality implies the Chinese remainder theorem,” Lect. Notes Math.,854, 124–126 (1981).

    Google Scholar 

  182. B. H. Dayton and L. G. Roberts, “K1 of n lines in the plane,” J. Pure Appl. Algebra,15, No. 1, 1–9 (1979).

    Google Scholar 

  183. B. H. Dayton and L. G. Roberts, “Seminormality of unions of planes,” Lect. Notes Math.,854, 93–123 (1981).

    Google Scholar 

  184. B. H. Dayton and C. A. Wiebel, “K-theory of hyperplanes,” Trans. Am. Math. Soc.,257, No. 1, 119–141 (1980).

    Google Scholar 

  185. B. H. Dayton and C. A. Wiebel, “Spectral sequences for the K-theory of glued rings,” Math. Rep. Acad. Sci. Can.,2, No. 2, 67–71 (1980).

    Google Scholar 

  186. B. H. Dayton and C. A. Wiebel,” A spectral sequence for the K-theory of affine glued schemes,” Lect. Notes Math.,854, 24–92 (1981).

    Google Scholar 

  187. R. K. Dennis, “The GE2-property for discrete subrings of C,” Proc. Am. Math. Soc.,50, 77–82 (1975).

    Google Scholar 

  188. R. K. Dennis, “Stability for K2,” Lect. Notes Math.,353, 85–94 (1973).

    Google Scholar 

  189. R. K. Dennis, M. E. Keating, and M. R. Stein, “Lower bounds for the order of K2 (ZG) and Wh2(G),” Math. Ann.,223, No. 2, 97–103 (1976).

    Google Scholar 

  190. R. K. Dennis and M. I. Krusemeyer, “K2(A[X, Y]/XY), a problem of Swan, and related computations,” J. Pure Appl. Algebra,15, No. 2, 125–148 (1979).

    Google Scholar 

  191. R. K. Dennis and A. R. Magid, “K2 of von Neumann regular rings,” J. Pure Appl. Algebra,6, No. 1, 49–59 (1975).

    Google Scholar 

  192. R. K. Dennis and M. R. Stein, “K2 of discrete valuation rings,” Adv. Math.,18, No. 2, 182–238 (1975).

    Google Scholar 

  193. R. K. Dennis and M. R. Stein, “Injective stability for K2 of local rings,” Bull. Am. Math. Soc.,80, No. 5, 1010–1013 (1974).

    Google Scholar 

  194. R. K. Dennis and M. R. Stein, “The functor K2: a survey of computations and problems,” Lect. Notes Math.,342, 243–280 (1973).

    Google Scholar 

  195. R. K. Dennis and M. R. Stein, “A new exact sequence for K2 and some consequences for rings of integers,” Bull. Am. Math. Soc.,78, No. 4, 600–603 (1972).

    Google Scholar 

  196. Dix exposés sur la cohomologie des schemas par J. Giraud, A. Grothendieck, S. L. Kleiman, M. Raynaud et J. Tate, North-Holland, Amsterdam (1968).

  197. A. Dold, “Algebraic K-theory of nonadditive functors of finite degree,” London Math. Soc. Lecture Note Ser., No. 11, 19–26 (1974).

    Google Scholar 

  198. P. Draxl, “SK1 von Algebren über vollstandig diskret bewerteten Körpern und Galoiskohomologie abelscher Körpererweiterungen,” J. Reine Angew. Math.,293–294, 116–142 (1977).

    Google Scholar 

  199. P. Draxl and M. Kneser (eds.), SK1 von Schiefkörpern, Springer-Verlag, Berlin (1980).

    Google Scholar 

  200. A. W. Dress, “The weak local global principle in algebraic K-theory,” Commun. Algebra,3, No. 7, 615–661 (1975).

    Google Scholar 

  201. A. W. M. Dress, “Contributions to the theory of induced representations,” Lect. Notes Math.,342, 183–240 (1973).

    Google Scholar 

  202. M. J. Dunwoody, “K2 of a Euclidean ring,” J. Pure Appl. Algebra,7, No. 1, 53–58 (1976).

    Google Scholar 

  203. M. J. Dunwoody, “K2 (Zπ) for π a group of order two or three,” J. London Math. Soc.,11, No. 4, 481–490 (1975).

    Google Scholar 

  204. W. G. Dwyer, “Twisted homological stability for general linear groups,” Ann. Math.,111, No. 2, 239–251 (1980).

    Google Scholar 

  205. B. Eckmann, “Some recent developments in the homology theory of groups (groups of finite and virtually finite dimension),” J. Pure Appl. Algebra,19, 61–75 (1980).

    Google Scholar 

  206. D. Eisenbud, “Solution du probleme de Serre par Quillen-Suslin,” Lect. Notes Math.,586, 9–19 (1977).

    Google Scholar 

  207. D. Eisenbud and E. Graham Evans, Jr., “Three conjectures about modules over polynomial rings,” Lect. Notes Math.,311, 78–89 (1973).

    Google Scholar 

  208. D. Eisenbud and E. Graham Evans, Jr., “Basic elements: theorems from algebraic K-theory,” Bull. Am. Math. Soc.,78, No. 4, 546–549 (1972).

    Google Scholar 

  209. R. Elman and T. Y. Lam, “On the quaternion symbol homomorphism gF:k2(F)→B(F),” Lect. Notes Math.,342, 447–463 (1973).

    Google Scholar 

  210. R. Elman and T. Y. Lam, “Determination of kn (n ⩾ 3) for global fields,” Proc. Am. Math. Soc.,31, No. 2, 427–428 (1972).

    Google Scholar 

  211. R. Elman and T. Y. Lam, “Pfister forms and K-theory of fields,” J. Algebra,23, No. 1, 181–213 (1972).

    Google Scholar 

  212. E. Endo, “Projective modules over polynomial rings,” J. Math. Soc. Jpn.,15, 339–352 (1963).

    Google Scholar 

  213. E. Enochs, “A proposition of Bass and the functional theorem of algebraic K-theory,” Arch. Math.,29, No. 4, 410–412 (1977).

    Google Scholar 

  214. L. Evens and E. M. Friedlander, “Kr(Z/p2) and Kr(Z/p[ε]) for p ⩾ 5 and r ≤4,” Bull. Am. Math. Soc.,2, No. 3, 440–443 (1980).

    Google Scholar 

  215. F. T. Farrell, “The nonfiniteness ofNil,” Proc. Am. Math. Soc.,65, No. 2, 215–216 (1977).

    Google Scholar 

  216. F. T. Farrell and W. G. Hsiang, “A formula for K1R2[T],” Proc. Symp. Pure Math.,17, 192–218 (1970).

    Google Scholar 

  217. F. T. Farrel and J. B. Wagoner, “Infinite matrices in algebraic K-theory and topology,” Comment. Math. Helv.,47, No. 4, 474–501 (1972).

    Google Scholar 

  218. D. Ferrand, “Les modules projectifs de type fini sur un anneau de polynômes sur un corps sont libres (d'apres Quillen et Suslin),” Lect. Notes Math.,567, 202–221 (1977).

    Google Scholar 

  219. Z. Fiedorowicz, “A note on the spectra of algebraic K-Theory,” Topology,16, No. 4, 417–421 (1977).

    Google Scholar 

  220. Z. Fiedorowicz and S. Priddy, “Loop spaces and finite orthogonal groups,” Bull. Am. Math. Soc.,81, No. 4, 700–702 (1975).

    Google Scholar 

  221. Z. Fiedorowicz and S. Priddy, Homology ofClassical Groups over Finite Fields and Their Associated Infinite Loop Spaces, Springer-Verlag, Berlin (1978).

    Google Scholar 

  222. R. Fossum, H.-B. Foxby, and B. Iversen, “A characteristic class in algebraic K-theory,” Prepr. Ser. Mat. Inst. Aarhus Univ., No. 29 (1978–79).

  223. E. M. Friedlander, “Computations of K-theories of finite fields,” Topology,15, No. 1, 87–109 (1975).

    Google Scholar 

  224. E. M. Friedlander, “Unstable K-theories of the algbraic closure of a finite field,” Comment. Math. Helv.,50, No. 2, 145–154 (1975).

    Google Scholar 

  225. E. M. Friedlander, “Etale K-theory I: Connections with etale cohomology and algebraic vector bundles,” Invent. Math.,60, No. 2, 105–134 (1980).

    Google Scholar 

  226. E. M. Friedlander, “The etale homotopy theory of a geometric fibration,” Manuscr. Math.,10, No. 3, 209–244 (1973).

    Google Scholar 

  227. E. M. Friedlander, “Homological stability for classical groups over finite fields,” Lect. Notes Math.,551, 290–302 (1976).

    Google Scholar 

  228. E. M. Friedlander and B. Parshall, “Etale cohomology of reductive groups,” Lect. Notes Math.,854, 127–140 (1981).

    Google Scholar 

  229. E. M. Friedlander and S. Priddy, “Karoubi's conjecture for finite fields,” J. Pure Appl. Algebra,10, No. 3, 233–238 (1977).

    Google Scholar 

  230. A. Fröhlich, “Non-Abelian Homological Algebra; I. Derived functors and satellites; II. Varieties; III. The functors EXT and TOR,” Proc. London. Math. Soc.,11, No. 42, 239–275 (1961);12, No. 45, 1–28 (1962);12, No. 48, 739–768 (1962).

    Google Scholar 

  231. A. Fröhlich and C. T. C. Wall, “Foundations of equivariant algebraic K-theory,” Lect. Notes Math.,108, 12–27 (1969).

    Google Scholar 

  232. W. Fulton and R. MacPherson, Intersecting cycles on algebraic variety. Preprint Ser. Mat. Inst. Aarhus Univ., No. 14 (1976).

  233. M. R. Gabel, “Lower bounds of the stable range of polynomial rings,” Pac. J. Math.,61, No. 1, 117–120 (1975).

    Google Scholar 

  234. M. R. Gabel and A. V. Geramita, “Stable range for matrices,” Queen's Papers in Pure and Appl. Math., No. 41, 120–147 (1974).

    Google Scholar 

  235. M. R. Gabel and A. V. Geramita, “Stable range for matrices,” J. Pure Appl. Algebra,5, No. 1, 97–112 (1974).

    Google Scholar 

  236. M. R. Gabel and A. V. Geramita, “Stable range for matrices (Erratum),” J. Pure Appl. Algebra,7, No. 2, 239 (1976).

    Google Scholar 

  237. P. Gabriel and M. Zisman, Calculus of Fractions and Homotopy Theory, Springer-Verlag, New York (1967).

    Google Scholar 

  238. H. Garland, “A finiteness theorem for K2 of a number field,” Ann. Math.,94, No. 3, 534–548 (1971).

    Google Scholar 

  239. S. C. Geller, “On the GEn of a ring,” Illinois J. Math.,21, No. 1, 109–112 (1977).

    Google Scholar 

  240. S. C. Geller and L. G. Roberts, “Kahler differentials and excision for curves,” J. Pure Appl. Algebra,17, No. 1, 85–112 (1980).

    Google Scholar 

  241. S. C. Geller and L. G. Roberts, “Excision and K1 regularity for curves with normal crossings,” J. Pure Appl. Algebra,15, No. 1, 11–21 (1979).

    Google Scholar 

  242. S. C. Geller and L. G. Roberts, “The relationship between the Picard groups and SK1 of some algebraic curves,” J. Algebra,55, No. 2, 213–230 (1978).

    Google Scholar 

  243. S. C. Geller and C. A. Wiebel, “K2 measures excision for K1,” Proc. Am. Math. Soc.,80, No. 1, 1–9 (1980).

    Google Scholar 

  244. S. M. Gersten, K-theory and algebraic cycles. Proc. Internat. Congress Math., Vancouver 1974, Vol. 2, S. 1 (1975), pp. 309–314.

    Google Scholar 

  245. S. M. Gersten, “The localization theorem for projective modules,” Commun. Algebra,2, No. 4, 307–350 (1974).

    Google Scholar 

  246. S. M. Gersten, “Higher K-theory of rings,” Lect. Notes Math.,341, 3–42 (1973).

    Google Scholar 

  247. S. M. Gersten, “Problems about higher K-functors,” Lect. Notes Math.,341, 43–56 (1973).

    Google Scholar 

  248. S. M. Gersten, “Some exact sequences in the higher K-theory of rings,” Lect. Notes Math.,341, 211–243 (1973).

    Google Scholar 

  249. S. M. Gersten, “A Mayer—Vietoris sequence in the K-theory of localizations,” J. Pure Appl. Algebra,2, No. 3, 275–285 (1972).

    Google Scholar 

  250. S. M. Gersten, “Higher K-theory for regular schemes,” Bull. Am. Math. Soc.,79, No. 1, 193–196 (1973).

    Google Scholar 

  251. S. M. Gersten, “K3 of a ring is H3 of the Steinberg group,” Proc. Am. Math. Soc.,37, No. 2, 366–368 (1973).

    Google Scholar 

  252. S. M. Gersten, “On the K-theory of Laurent polynomials,” Proc. Am. Math. Soc.,30, No. 2, 223–228 (1971).

    Google Scholar 

  253. S. M. Gersten, “On the functor K2,” J. Algebra,17, No. 2, 212–237 (1971).

    Google Scholar 

  254. S. M. Gersten, “On Mayer—Vietoris functors and algebraic K-theory,” J. Algebra,18, No. 1, 51–88 (1971).

    Google Scholar 

  255. S. M. Gersten, “Homotopy theory of rings,” J. Algebra,19, No. 3, 396–415 (1971).

    Google Scholar 

  256. S. M. Gersten, “On the spectrum of algebraic K-theory,” Bull. Am. Math. Soc.,78, No. 2, 216–219 (1972).

    Google Scholar 

  257. S. M. Gersten, “On class groups of free products,” Ann. Math.,87, No. 2, 392–398 (1968).

    Google Scholar 

  258. S. M. Gersten, “K-theory of free rings,” Commun. Algebra,1, 39–64 (1974).

    Google Scholar 

  259. S. M. Gersten and D. L. Rector, “A relation between two simplicial algebraic K-theories,” Bull. Am. Math. Soc.,77, No. 3, 397–399 (1971).

    Google Scholar 

  260. C. H. Giffen, “Hermitian forms and higher algebraic K-theory,” Bull. Am. Math. Soc.,83, No. 6, 1303–1305 (1977).

    Google Scholar 

  261. H. Gillet, “Riemann—Roch theorems for higher algebraic K-theory,” Bull. Am. Math. Soc.,3, No. 2, 849–852 (1980).

    Google Scholar 

  262. H. Gillett, “Comparison of K-theory spectral sequences with applications,” Lect. Notes Math.,854, 141–167 (1981).

    Google Scholar 

  263. D. R. Grayson, “K-theory and localization of noncommutative rings,” J. Pure Appl. Algebra,18, No. 2, 125–127 (1980).

    Google Scholar 

  264. D. R. Grayson, “Algebraic cycles and algebraic K-theory,” J. Algebra,61, No. 1, 129–151 (1979).

    Google Scholar 

  265. D. R. Grayson, “Localization for flat modules in algebraic K-theory,” J. Algebra,61, No. 2, 463–496 (1979).

    Google Scholar 

  266. D. R. Grayson, “K2 and the K-theory of automorphisms,” J. Algebra,58, No. 1, 12–30 (1979).

    Google Scholar 

  267. D. R. Grayson, “Products in K-theory and intersecting algebraic cycles,” Invent. Math.,47, No. 1, 71–83 (1978).

    Google Scholar 

  268. D. R. Grayson, “Projections, cycles and algebraic K-theory,” Math. Ann.,234, No. 1, 69–72 (1978).

    Google Scholar 

  269. D. R. Grayson, “The K-theory of hereditary categories,” J. Pure Appl. Algebra,11, Nos. 1–3 67–74 (1977).

    Google Scholar 

  270. D. R. Grayson, “The K-theory of endomorphisms,” J. Algebra,48, No. 2, 439–446 (1977).

    Google Scholar 

  271. D. R. Grayson, “Higher algebraic K-theory: II (after Daniel Quillen),” Lect. Notes Math.,551, 217–240 (1976).

    Google Scholar 

  272. D. R. Grayson, “Dilogarithm computations for K3,” Lect. Notes Math.,854, 168–178 (1981).

    Google Scholar 

  273. S. M. Green, “Generators and relations for the special linear group over a division ring,” Proc. Am. Math. Soc.,62, No. 2, 229–232 (1977).

    Google Scholar 

  274. S. M. Green, “Generators and relations for K2 of a division ring,” Lect. Notes Math.,551, 74–76 (1976).

    Google Scholar 

  275. S. M. Green, D. Handelman, and P. Roberts, “K-theory of finite dimensional division algebras,” J. Pure Appl. Algebra,12, No. 2, 153–158 (1978).

    Google Scholar 

  276. R. Greenberg, “A note on K2 and the theory of Zp-extensions,” Am. J. Math.,100, No. 6, 1235–1245 (1978).

    Google Scholar 

  277. D. Guin, “K-theory algebrique et invariants des formes quadratiques,” Bull Soc. Math. France Mem., No. 59, 69–94 (1979).

    Google Scholar 

  278. D. Guin, “Une suite spectrale en K-théorie hermitienne. Invariants des formes quadratiques,” C. R. Acad. Sci. Paris,286, No. 17, A727-A729 (1978).

    Google Scholar 

  279. D. Guin-Waléry and J. L. Loday, “Obstruction a l'excision en K-theorie algebrique,” Lect. Notes Math.,854, 179–216 (1981).

    Google Scholar 

  280. R. Gustafson, “The degenerate principal series for Sp(2n),” Mem. Am. Math. Soc., No. 248 (1981).

  281. W. H. Gustafson, P. R. Halmos, and J. M. Zelmanowitz, “The Serre conjecture,” Am. Math. Monthly,85, No. 5, 357–359 (1978).

    Google Scholar 

  282. G. Harder, “Die Kohomologie S-arithmetischer Gruppen über Funktionenkörpern,” Invent. Math.,42, 135–175 (1977).

    Google Scholar 

  283. G. Harder, “On the cohomology of SL(2,R),” in: Lie Groups and Their Representations, Budapest (1975), pp. 139–150.

  284. B. Harris and G. Segal, “Ki groups of rings of algebraic integers,” Ann. Math.,101, No. 1, 20–33 (1975).

    Google Scholar 

  285. B. Harris and J. Stasheff, “Suspension, automorphisms, and division algebras,” Lect. Notes Math.,342, 337–346 (1973).

    Google Scholar 

  286. A. E. Hatcher, “Pseudoisotopy and K2,” Lect. Notes Math.,342, 328–336 (1973).

    Google Scholar 

  287. J.-C. Hausmann, “Algebraic K-theory and flat manifolds,” Lect. Notes Math.,763, 212–234 (1979).

    Google Scholar 

  288. J.-C. Hausmann, “Stabilité partielle pour l'homologie de groupes spéciaux linéaires,” C. R. Acad. Sci. Paris,281, No. 16, A687-A690 (1975).

    Google Scholar 

  289. J.-C. Hausmann, “Homology sphere bordism and Quillen plus construction,” Lect. Notes Math.,551, 170–181 (1976).

    Google Scholar 

  290. A. Heller, “Some exact sequences in algebraic K-theory,” Topology,3, 389–408 (1965).

    Google Scholar 

  291. A. Heller and I. Reiner, “Grothendieck groups of orders in semisimple algebras,” Trans. Am. Math. Soc.,112, No. 2, 344–355 (1964).

    Google Scholar 

  292. H. Bass (ed.), Algebraic K-Theory III. Hermitian K-Theory and Geometric Applications (Lecture Notes in Mathematics, Vol. 343), Springer-Verlag, Berlin (1973).

    Google Scholar 

  293. H. Bass (ed.), Algebraic K-Theory I. Higher K-Theories (Lecture Notes in Mathematics, Vol. 341), Springer-Verlag, Berlin (1973).

    Google Scholar 

  294. R. Hoobler and D. L. Rector, “Arithmetic K-theory,” Lect. Notes Math.,418, 78–95 (1974).

    Google Scholar 

  295. G. Horrocks, “Projective modules over extension of a local ring,” Proc. London Math. Soc.,14, No. 56, 714–718 (1964).

    Google Scholar 

  296. J. Hurrelbrink, “On K2(0) and presentation of SLn (0) in the real quadratic case,” J. Reine Angew. Math.,319, 213–220 (1980).

    Google Scholar 

  297. J. Hurrelbrink, “The elements ofK 2(Zs),” Manuscr. Math.,24, No. 2, 173–177 (1978).

    Google Scholar 

  298. J. Hurrelbrink and U. Rehmann, “Zur endlichen Präsentation von Chevalley-Gruppen über den euklidischen imaginär-quadratischen Zahlringen,” Arch. Math. (Basel),27, No. 2, 123–133 (1976).

    Google Scholar 

  299. L. Illusie, “Travaux de Quillen sur la cohomologie des groupes,” Lect. Notes Math.,317, 89–105 (1973).

    Google Scholar 

  300. F. Ischebeck, “Hauptidealringe mit nichttrivialer SK1-Gruppe,” Arch. Math.,35, Nos. 1–2, 138–139 (1980).

    Google Scholar 

  301. J. P. Jouanolou, “Comparison des K-théories algébriques et topologique de quelques variétés algébriques,” C. R. Acad. Sci. Paris,272, No. 21, A1373-A1375 (1971).

    Google Scholar 

  302. J. P. Jouanolou, “Quelques calculs en K-theorie des schemas,” Lect. Notes Math.,341, 317–334 (1973).

    Google Scholar 

  303. J. P. Jouanolou, “Une suite exacte de Mayer-Vietoris en K-theorie algebrique,” Lect. Notes Math.,341, 293–316 (1973).

    Google Scholar 

  304. W. van der Kallen, “Le K2 de nombres duaux,” C. R. Acad. Sci. Paris,273, No. 25, A1204-A1207 (1971).

    Google Scholar 

  305. W. van der Kallen, “The Schur multipliers of SL(3,Z) and SL(4, Z),” Math. Ann.,212, No. 1, 47–49 (1974).

    Google Scholar 

  306. W. van der Kallen, “Injective stability for K2,” Lect. Notes Math.,551, 77–154 (1976).

    Google Scholar 

  307. W. van der Kallen, “Another presentation for Steinberg groups,” Indag. Math.,39, No. 4, 304–312 (1977).

    Google Scholar 

  308. W. van der Kallen, “The K2 of rings with many units,” Ann. Sci. Ecole Norm. Sup.,10, No. 4, 473–515 (1977).

    Google Scholar 

  309. W. van der Kallen, “Generators and relations in algebraic K-theory,” in: Proc. Int. Congr. Math. (Helsinki 1978), Acad. Sci. Fennica, Helsinki (1980), Vol. 1, pp. 305–310.

    Google Scholar 

  310. W. van der Kallen, “Homology stability for linear groups,” Invent. Math.,60, No. 3, 269–295 (1980).

    Google Scholar 

  311. W. van der Kallen, “Stability for K2 of Dedekind rings of arithmetic type,” Lect. Notes Math.,854, 217–248 (1981).

    Google Scholar 

  312. W. van der Kallen, H. Maazen, and J. Stientstra, “A presentation for some K2(n, R),” Bull. Am. Math. Soc.,81, No. 5, 934–936 (1975).

    Google Scholar 

  313. W. van der Kallen and M. R. Stein, “On the Schur multipliers of Steinberg and Chevalley groups over commutative rings,” Math. Z.,155, No. 1, 83–94 (1977).

    Google Scholar 

  314. Ming-Chang Kang, “Projective modules over some polynomial rings,” J. Algebra,59, No. 1, 65–76 (1979).

    Google Scholar 

  315. M. Karoubi, “Algèbres de Clifford et K-theorie,” Ann. Sci. Ecole Norm. Sup.,1, No. 2, 161–270 (1968).

    Google Scholar 

  316. M. Karoubi, “Sur la K-theorie algebrique,” Ann. Sci. Ecole Norm. Sup.,1, 581–616 (1968).

    Google Scholar 

  317. M. Karoubi, “Sur la K-theorie equivariante,” Lect. Notes Math.,136, 187–253 (1970).

    Google Scholar 

  318. M. Karoubi, “Foncteurs derives et K-theorie,” Lect. Notes Math.,136, 107–186 (1970).

    Google Scholar 

  319. M. Karoubi, “La périodicité de Bott en K-théorie générale,” Ann. Sci Ecole Norm. Sup.,4, No. 1, 63–95 (1971).

    Google Scholar 

  320. M. Karoubi, “Some problems and conjectures in algebraic K-theory,” Lect. Notes Math.,343, 52–56 (1973).

    Google Scholar 

  321. M. Karoubi, “K-theorie algebrique. Sur l'ordre de K3(Z),” C. R. Acad. Sci. Paris,A278, No. 2, 67–69 (1974).

    Google Scholar 

  322. M. Karoubi, “Localisation de formes quadratiques. I,” Ann. Sci. Ecole Norm. Sup.,7, No. 3, 359–403 (1974).

    Google Scholar 

  323. M. Karoubi, “Localisation de formes quadratiques. II,” Ann. Sci. Ecole Norm. Sup.,8, No. 1, 99–155 (1975).

    Google Scholar 

  324. M. Karoubi, “Le théorème fondamental de la K-théorie hermitienne,” Ann. Math.,112, No. 2, 259–282 (1980).

    Google Scholar 

  325. M. Karoubi, “Theorie de Quillen et homologie du groupe orthogonal,” Ann. Math.,112, No. 2, 207–257 (1980).

    Google Scholar 

  326. M. Karoubi and O. E. Villamayor, “K-théorie algébrique et K-théorie topologique. I,” Math. Scand.,28, No. 2, 265–307 (1971).

    Google Scholar 

  327. M. Karoubi and O. E. Villamayor, “K-théorie algébrique et K-théorie topologique. II,” Math. Scand.,32, No. 1, 57–86 (1973).

    Google Scholar 

  328. Chr. Kassel, “Un calcul d'homologie du groupe linéaire général,” C. R. Acad. Sci. Paris,A288, No. 9, 481–483 (1979).

    Google Scholar 

  329. Chr. Kassel, “Homologie du groupe linéaire général et K-theorie stable,” C. R. Acad. Sci. Paris,290, No. 22, A1041-A1044 (1980).

    Google Scholar 

  330. Chr. Kassel, “K-théorie relative d'un ideal bilatère de carré nul: étude homologique en basse dimension,” Lect. Notes Math.,854, 249–261 (1981).

    Google Scholar 

  331. K. Kato, “A generalization of local class field theory by using K-groups. I,” J. Fac. Sci. Univ. Tokyo Sect. IA Math.,26, No. 2, 303–376 (1979).

    Google Scholar 

  332. K. Kato, “A generalization of local class field theory by using K-groups. II,” J. Fac. Sci. Univ. Tokyo Sect. IA Math.,27, No. 3, 603–683 (1980).

    Google Scholar 

  333. M. E. Keating, “Whitehead groups of some metacyclic groups and orders,” J. Algebra,22, No. 2, 332–349 (1972).

    Google Scholar 

  334. M. E. Keating, “On the K-theory of the quaternion group,” Mathematika,20, No. 1, 59–62 (1973).

    Google Scholar 

  335. M. E. Keating, “Values of tame symbols on division algebras,” J. London Math. Soc.,14, No. 1, 25–30 (1976).

    Google Scholar 

  336. M. E. Keating, “A transfer map in K-theory,” J. London Math. Soc.,16, No. 1, 38–42 (1977). (1977).

    Google Scholar 

  337. M. A. Kervaire, “Multiplicateurs de Schur et K-theorie,” in: Essays on Topology and Related Topics, Springer-Verlag, New York (1970), pp. 212–225.

    Google Scholar 

  338. M. A. Kervaire and M. Pavaman Murthy, “On the projective class group of cyclic groups of prime power order,” Comment. Math. Helv.,52, No. 3, 415–452 (1977).

    Google Scholar 

  339. F. Keune, “Algèbre homotopique et K-théorie algébrique,” C. R. Acad. Sci. Paris,273, No. 14, A592-A595 (1971).

    Google Scholar 

  340. F. Keune, “Derived functors and algebraic K-theory,” Lect. Notes Math.,341, 166–176 (1973).

    Google Scholar 

  341. F. Keune, “(t2−t)-reciprocities on the affine line and Matsumoto's theorem,” Invent. Math.,28, No. 2, 185–192 (1975).

    Google Scholar 

  342. F. Keune, “The relativization of K2,” J. Algebra,54, No. 1, 159–177 (1978).

    Google Scholar 

  343. F. Keune, “Doubly relative K-theory and the relative K3,” J. Pure Appl. Algebra,20, No. 1, 39–53 (1981).

    Google Scholar 

  344. S. Klasa, “On Steinberg groups,” Lect. Notes Math.,353, 131–138 (1973).

    Google Scholar 

  345. M. Kneser, “Das Kongruenz Untergruppenproblem für orthogonale Gruppen,” Sitzungsber. Berlin Math. Gesellschaft (1969–1971).

  346. M. A. Knus and M. Ojanguren, “Modules and quadratic forms over polynomial algebras,” Proc. Am. Math. Soc.,66, No. 2, 223–226 (1977).

    Google Scholar 

  347. M. A. Knus, M. Ojanguren, and R. Sridharan, “Quadratic forms and Azumaya algebras,” J. Reine Angew. Math.,303-304, 231–248 (1978).

    Google Scholar 

  348. K. Kramer and A. Candiotti, “On K2 and ZZ extensions of number fields,” Am. J. Math.,100, No. 1, 177–196 (1978).

    Google Scholar 

  349. Ch. Kratzer, “Operations d'Adams en K-théorie algébrique,” C. R. Acad. Sci. Paris,287, No. 5, A297-A298 (1978).

    Google Scholar 

  350. Ch. Kratzer, “λ-structure en K-théorie algébrique,” Comment. Math. Helv.,55, No. 2, 233–254 (1980).

    Google Scholar 

  351. M. I. Krusemeyer, “Fundamental groups, algebraic K-theory, and a problem of Abhyankar,” Invent. Math.,19, No. 1, 15–47 (1973).

    Google Scholar 

  352. M. I. Krusemeyer, “Completing α2, β, γ,” Queen's Papers in Pure and Appl. Math., No. 42, 253–254 (1975).

    Google Scholar 

  353. A. O. Kuku, “Whitehead group of orders in p-adic semisimple algebras,” J. Algebra,25, No. 3, 415–418 (1973).

    Google Scholar 

  354. A. O. Kuku, “Some algebraic K-theoretic applications of the LF and NF functors,” Proc. Am. Math. Soc.,37, No. 2, 363–365 (1973).

    Google Scholar 

  355. A. O. Kuku, “SKn of orders and Gn of finite rings,” Lect. Notes Math.,551, 60–68 (1976).

    Google Scholar 

  356. A. S. Küsefoglu, “The second degree cohomology of finite orthogonal groups. II,” J. Algebra,67, No. 1, 88–109 (1980).

    Google Scholar 

  357. J. Labute and P. Russel, “On K2 of truncated polynomial rings,” J. Pure Appl. Algebra,6, No. 3, 239–251 (1975).

    Google Scholar 

  358. T. Y. Lam, The Algebraic Theory of Quadratic Forms, Benjamin, Reading (1973).

    Google Scholar 

  359. T. Y. Lam, Serre's Conjecture, Springer-Verlag, Berlin (1978).

    Google Scholar 

  360. T. Y. Lam and M. K. Siu, “K0 and K1 — an introduction to algebraic K-theory,” Am. Math. Mon.,82, No. 4, 329–364 (1975).

    Google Scholar 

  361. J. Larotonda and A. Micali, “Espaces classifiants pour les foncteurs K−n,” C. R. Acad. Sci. Paris,272, No. 18, A1162-A1165 (1971).

    Google Scholar 

  362. R. Lee and R. H. Szczarba, “On algebraic K-theory and the homology of congruence subgroups,” Lect. Notes Math.,575, 78–87 (1975).

    Google Scholar 

  363. R. Lee, “On unstable cohomology classes of SLn(Z),” Proc. Nat. Acad. Sci. U.S.A.,75, No. 1, 43–44 (1978).

    Google Scholar 

  364. R. Lee and R. H. Szczarba, “The group K3(Z) is cyclic of order forty-eight,” Ann. Math.,104, No. 1, 31–60 (1976).

    Google Scholar 

  365. R. Lee and R. H. Szczarba, “On the homology of congruence subgroups and K3(Z),” Proc. Nat. Acad. Sci. U.S.A.,72, No. 2, 651–653 (1975).

    Google Scholar 

  366. R. Lee and R. H. Szczarba, “On the torsion in K4(Z) and K5(Z),” Duke Math. J.,45, No. 1, 101–129 (1978).

    Google Scholar 

  367. Y. Lequain and A. Simis, Projective modules over R[X1, …, Xn], R a Prüfer domain, Notas e Commun. Mat., No. 84 (1978).

  368. Y. Lequain and A. Simis, “Projective modules over R[X1, …, Xn], R a Prüfer domain,” J. Pure Appl. Algebra,18, No. 2, 165–171 (1980).

    Google Scholar 

  369. S. Lichtenbaum, “Values of zeta-function, etale cohomology, and algebraic K-theory,” Lect. Notes Math.,342, 489–501 (1973).

    Google Scholar 

  370. H. Lindel, “Projektive Moduln über Polynomringen A[T1, …,Tm] mit einem regulären Grundring A,” Manuscr. Math.,23, No. 2, 143–154 (1978).

    Google Scholar 

  371. H. Lindel, “Erweiterungskriterien für stabil freie Moduln über Polynomringen,” Math. Ann.,250, No. 2, 99–108 (1980).

    Google Scholar 

  372. H. Lindel, “On the Bass-Quillen conjecture concerning projective modules over polynomial rings,” Invent. Math., 65, No. 2, 319–323 (1981).

    Google Scholar 

  373. H. Lindel and W. Lutkebohmert, “Projektive Moduln über polynomialen Erweiterungen von Potenzreihenalgebren,” Arch. Math. (Basel),28, No. 1, 51–54 (1977).

    Google Scholar 

  374. J.-L. Loday, “Applications algebriques du tore dans la sphere et de Sp × Sq dans Sp+q,” Lect. Notes Math.,342, 79–91 (1973).

    Google Scholar 

  375. J.-L. Loday, “Structure multiplicative en K-théorie algébrique,” C. R. Acad. Sci. Paris,A279, No. 9, 321–324 (1974).

    Google Scholar 

  376. J.-L. Loday, “K-théorie algébrique et représentations de groupes,” Ann. Sci. Ecole Norm. Sup.,9, No. 3, 309–377 (1976).

    Google Scholar 

  377. J.-L. Loday, “Les matrices monomiales et le groupe de Whitehead Wh2,” Lect. Notes Math.,551, 155–163 (1976).

    Google Scholar 

  378. J.-L. Loday, “Higher Witt groups: A survey,” Lect. Notes Math.,551, 311–335 (1976).

    Google Scholar 

  379. J.-L. Loday, “Cohomologie et groupe de Steinberg relatifs,” J. Algebra,54, No. 1, 178–202 (1978).

    Google Scholar 

  380. J.-L. Loday, “On the boundary map K3(λ/I) → K2(Λ, I),” Lect. Notes Math.,854, 262–268 (1981).

    Google Scholar 

  381. J.-L. Loday, “Symboles en K-théorie algébrique supérieure,” C. R. Acad. Sci. Paris, Ser. I Math.,292, No. 18, 863–866 (1981).

    Google Scholar 

  382. H. Maazen, Stabilite de l'homologie de GLn,” C. R. Acad. Sci. Paris,288, No. 15, A707-A708 (1979).

    Google Scholar 

  383. H. Maazen and J. Stienstra, “A presentation for K2 of split radical pairs,” J. Pure Appl. Algebra,10, No. 3, 271–294 (1977).

    Google Scholar 

  384. A. R. Magid, “K-theory of commutative regular rings,” Proc. Am. Math. Soc.,39, No. 3, 489–492 (1973).

    Google Scholar 

  385. B. Margurn, “SK1 of dihedral groups,” J. Algebra,51, No. 2, 399–415 (1978).

    Google Scholar 

  386. B. A. Magurn, “Images of SK1ZG,” Pac. J. Math.,79, No. 2, 531–539 (1978).

    Google Scholar 

  387. B. A. Magurn, “Whitehead groups of some hyperelementary groups,” J. London Math. Soc.,21, No. 1, 176–188 (1980).

    Google Scholar 

  388. P. Maroscia, “Modules projectifs sur certains anneaux de polynômes,” C. R. Acad. Sci. Paris,285, No. 4, A183-A185 (1977).

    Google Scholar 

  389. H. Matsumoto, “Sur les sous-groupes arithmétiques des groupes semisimples deployés,” Ann. Sci. Ecole Norm. Sup.,2, No. 1, 1–62 (1969).

    Google Scholar 

  390. J. P. May, Simplicial Objects in Algebraic Topology, Van Nostrand, Princeton (1967).

    Google Scholar 

  391. E. E. Mendoza, “Cohomology of PGL2 over imaginary quadratic integers,” Bonner Math. Schriften, No. 128 (1980).

  392. J. L. Mennicke, “Finite factor groups of the unimodular group,” Ann. Math.,81, No. 1, 31–37 (1965).

    Google Scholar 

  393. R. J. Milgram, “Odd index subgroups of units in cyclotomic fields and applications,” Lect. Notes Math.,854, 269–298 (1981).

    Google Scholar 

  394. J. Milnor, “Algebraic K-theory and quadratic forms,” Invent. Math.,9, No. 4, 318–344 (1970).

    Google Scholar 

  395. J. Milnor, Introduction to Algebraic K-Theory, Princeton Univ. Press (1971).

  396. N. Mohan Kummar, “On two conjectures about polynomial rings,” Invent. Math.,46, No. 3, 225–236 (1978).

    Google Scholar 

  397. C. C. Moore, “Group extensions of p-adic and adelic linear groups,” Inst. Hautes Etudes Sci. Publ. Math., No. 35, 157–222 (1968).

    Google Scholar 

  398. R. A. Morris, “Derivatives of Witt vectors with application to K2 of truncated polynomial rings and Laurent series,” J. Pure Appl. Algebra,18, No. 1, 91–96 (1980).

    Google Scholar 

  399. M. P. Murthy, “Projective A[X]-modules,” J. London Math. Soc.,41, No. 3, 453–456 (1966).

    Google Scholar 

  400. M. P. Murthy, “Vector bundles over affine surfaces birationally equivalent to a ruled surface,” Ann. Math.,89, No. 2, 242–253 (1970).

    Google Scholar 

  401. M. P. Murthy, “Complete intersections,” Queen's Papers Pure Appl. Math., No. 42, 197–211 (1975).

    Google Scholar 

  402. M. P. Murthy, “Affine varieties as complete intersections,” in: Proc. Int. Sympos. on Algebraic Geometry, Kyoto (1977), pp. 231–236.

  403. M. P. Murthy and C. Pedrini, “K0 and K1 of polynomial rings,” Lect. Notes Math.,342, 109–121 (1973).

    Google Scholar 

  404. M. P. Murthy and R. G. Swan, “Vector bundles over affine surfaces,” Invent. Math.,36, 125–165 (1976).

    Google Scholar 

  405. M. P. Murthy and J. Towber, “Algebraic vector bundles over A3 are trivial,” Invent. Math.,24, No. 3, 173–189 (1974).

    Google Scholar 

  406. A. Nobile and O. E. Villamayor, “Sur la K-théorie algébrique,” Ann. Sci. Ecole Norm. Sup.,1, No. 4, 581–616 (1968).

    Google Scholar 

  407. M. Ojanguren, “Formes quadratiques sur les algebres de polynomes,” C. R. Acad. Sci. Paris,287, No. 9, A695-A698 (1978).

    Google Scholar 

  408. M. Ojanguren and R. Sridharan, “Cancellation of Azumaya algebras,” J. Algebra,18, No. 4, 501–505 (1971).

    Google Scholar 

  409. R. Oliver, “SK1 for finite group rings: I, II, III,” Invent. Math.,57, No. 2, 183–204 (1980); Mat. Inst. Aarhus Univ., Preprint Ser. 1979/80, No. 25; Lecture Notes in Math.,854, 297–337 (1981).

    Google Scholar 

  410. R. Oliver, “SK1 of p-adic group rings,” Bull. Am. Math. Soc.,3, No. 2, 863–866 (1980).

    Google Scholar 

  411. F. Orecchia, “Su alcuni gruppi della K-teoria della varietà affini,” Ann. Mat. Pura Appl.,123, 203–217 (1980).

    Google Scholar 

  412. F. Orecchia, “Sui gruppi SK0 et NK0 di alcune superfici affini,” Boll. Un. Mat. Ital.,B17, No. 2, 528–538 (1980).

    Google Scholar 

  413. S. Parimala, “Projective modules and Hermitian matrices,” J. Pure Appl. Algebra,7, No. 1, 5–14 (1976).

    Google Scholar 

  414. S. Parimala, “Failure of a quadratic analogue of Serre's conjecture,” Am. J. Math.,100, No. 5, 913–924 (1978).

    Google Scholar 

  415. S. Parimala and R. Sridharan, “Projective modules over polynomial rings over division rings,” J. Math. Kyoto,15, 129–148 (1975).

    Google Scholar 

  416. S. Parimala and R. Sridharan, “Projective modules over quaternion algebras,” J. Pure Appl. Algebra,9, No. 2, 181–193 (1977).

    Google Scholar 

  417. Raman Parimala and R. Sridharan, “Quadratic forms over rings of dimension 1,” Comment. Math. Helv.,55, No. 4, 634–644 (1980).

    Google Scholar 

  418. C. Pedrini, “On the algebraic K-theory of affine curves,” Boll. Un. Mat. Ital.,9, No. 3, 856–873 (1974).

    Google Scholar 

  419. C. Pedrini, “Vector bundles over singular affine surfaces,” Boll. Un. Mat. Ital.,B17, No. 3, 1246–1255 (1980).

    Google Scholar 

  420. S. Priddy, “On a conjecture concerning K*(Z/p2),” Lect. Notes Math.,854, 338–342 (1981).

    Google Scholar 

  421. D. Quillen, “Projective modules over polynomial rings,” Invent. Math.,36, 167–171 (1976).

    Google Scholar 

  422. D. Quillen, “Cohomology of groups,” in: Actes Congr. Internat. Math. 1970, T. 2, Paris (1971), pp. 47–51.

    Google Scholar 

  423. D. Quillen, “On the cohomology and K-theory of the general linear groups over a finite field,” Ann. Math.,96, No. 3, 552–586 (1972).

    Google Scholar 

  424. D. Quillen, “Algebraic K-theory for category with exact sequences,” London Math. Soc. Lecture Note Ser.,11, 19–26 (1972).

    Google Scholar 

  425. D. Quillen, “Higher algebraic K-theory: I,” Lect. Notes Math.,341, 85–147 (1973).

    Google Scholar 

  426. D. Quillen, “Finite generation of the groups Ki of rings of algebraic integers,” Lect. Notes Math.,341, 179–198 (1973).

    Google Scholar 

  427. D. Quillen, “Higher algebraic K-theory,” in: Proc. Int. Congr. Math. Vancouver, Vol. 1, S. 1 (1974), pp. 171–176.

    Google Scholar 

  428. D. Quillen, “Letter from Quillen to Milnor on Im (πi0 → π pi → Ki(Z)),“ Lect. Notes Math.,551, 182–188 (1976).

    Google Scholar 

  429. D. Quillen, “Characteristic classes of representations,” Lect. Notes Math.,551, 189–216 (1976).

    Google Scholar 

  430. M. S. Raghunathan, “Principal bundles on the affine space,” in: Studies in Math., No. 8, Tata Inst. of Fundamental Research (1978), pp. 187–206.

    Google Scholar 

  431. M. S. Raghunathan, “On the congruence subgroup problem,” Inst. Hautes Etudes Sci. Publ. Math.,46, 107–162 (1976).

    Google Scholar 

  432. A. A. Ranicki, “Algebraic L-theory. I. Foundations,” Proc. London Math. Soc.,27, No. 1, 101–125 (1973).

    Google Scholar 

  433. A. A. Ranicki, “Algebraic L-theory. II. Laurent extensions,” Proc. London Math. Soc.,27, No. 1, 126–158 (1973).

    Google Scholar 

  434. A. A. Ranicki, “Algebraic L-theory. IV. Polynomial extension rings,” Comment. Math. Helv.,49, No. 2, 137–167 (1974).

    Google Scholar 

  435. A. Ranicki, “On the algebraic L-theory of semisimple rings,” J. Algebra,50, No. 1, 242–243 (1978).

    Google Scholar 

  436. A. Ranicki, “Localization in quadratic L-theory,” Lect. Notes Math.,741, 102–157 (1979).

    Google Scholar 

  437. A. Ranicki, “The algebraic theory of surgery; I. Foundations; II. Applications to topology,” Proc. London Math. Soc.,40, No. 2, 87–192, 193–283 (1980).

    Google Scholar 

  438. M. Raynaud, “Modules projectifs universels,” Invent. Math.,6, No. 1, 1–26 (1968).

    Google Scholar 

  439. U. Rehmann, “Zentrale Erweiterungen der speziellen linearen Gruppe eines Schiefkörpers,” J. Reine Angew. Math.,301, 77–104 (1978).

    Google Scholar 

  440. U. Rehmann and C. Soulé, “Finitely presented group of matrices,” Lect. Notes Math.,551, 164–169 (1976).

    Google Scholar 

  441. U. Rehmann and U. Stuhler, “On K2 of finite dimensional division algebras over arithmetical fields,” Invent. Math.,50, No. 1, 75–90 (1978).

    Google Scholar 

  442. I. Reiner, “Integral representations: genus, K-theory and class groups,” Lect. Notes Math.,697, 52–69 (1978).

    Google Scholar 

  443. L. G. Roberts, “K1 of some Abelian categories,” Trans. Am. Math. Soc.,138, 377–382 (1969).

    Google Scholar 

  444. L. Roberts, “Base change for K0 of algebraic varieties,” Lect. Notes Math.,342, 122–134 (1973).

    Google Scholar 

  445. L. Roberts, “Comparison of algebraic and topological K-theory,” Lect. Notes Math.,342, 74–78 (1973).

    Google Scholar 

  446. L. Roberts, “The K-theory of some reducible affine varieties,” Queen's Papers Pure Appl. Math., No. 41, 47–63 (1974).

    Google Scholar 

  447. L. G. Roberts, “K1 of a curve of genus zero,” Trans. Am. Math. Soc.,188, Issue 2, 319–326 (1974). 919

    Google Scholar 

  448. L. G. Roberts, “The K-theory of some reducible affine varieties. I,” J. Algebra,35, Nos. 1–3, 516–527 (1975).

    Google Scholar 

  449. L. G. Roberts, “The K-theory of some reducible affine curves: a combinatorial approach,” Lect. Notes Math.,551, 44–59 (1976).

    Google Scholar 

  450. L. G. Roberts, “K2 of some truncated polynomial rings,” Lect. Notes Math.,734, 249–278 (1979).

    Google Scholar 

  451. L. G. Roberts, “SK1 R[X, Y]/(X2 + Y2 −1); remarks on an example of Bass and Milnor,” Bol. Soc. Brasil. Mat.,10, No. 1, 77–82 (1979).

    Google Scholar 

  452. J. Rohlfs, “Über die Eindeutigkeit des Reziprozitätsgesetzes in der Klassenkörpertheorie,” Math. Ann.,200, No. 1, 95–97 (1973).

    Google Scholar 

  453. M. Roitman, “On Serre's problem on projective modules,” Proc. Am. Math. Soc.,50, 45–52 (1975).

    Google Scholar 

  454. M. Roitman, “A note on Quillen's paper 'Projective modules over polynomial rings,” Proc. Am. Math. Soc.,64, No. 2, 231–232 (1977).

    Google Scholar 

  455. M. Roitman, “On projective modules over polynomial rings,” J. Algebra,58, No. 1, 51–63 (1979).

    Google Scholar 

  456. A. Rosenberg, “The map from the Witt ring of a local field to the Witt ring of the quotient field,” Queen's Papers Pure Appl. Math., No. 41, 22–25 (1974).

    Google Scholar 

  457. S. Rosset, “Abelian splitting of division algebras of prime degrees,” Comment. Math. Helv.,52, No. 4, 519–523 (1977).

    Google Scholar 

  458. S. Rosset, “Generic matrices, K2, and unirational fields,” Bull. Am. Math. Soc.,81, No.4, 707–708 (1975).

    Google Scholar 

  459. Chih Han Sah and J. B. Wagoner, “Second homology of Lie groups made discrete,” Commun. Algebra,5, No. 6, 611–642 (1977).

    Google Scholar 

  460. A. Sathaye, “On the Forster-Eisenbud-Evans conjectures,” Invent. Math.,46, No. 3, 211–224 (1978).

    Google Scholar 

  461. I. Schellong, “Ein Kriterium für die Richtigkeit der Milnor-Vermutung,” Manuscr. Math.,15, No. 1, 81–89 (1975).

    Google Scholar 

  462. C. S. Seshadri, “Triviality of vector bundles over the affine space K2,” Proc. Nat. Acad. Sci. U.S.A.,44, 456–458 (1958).

    Google Scholar 

  463. G. Segal, “Classifying spaces and spectral sequences,” Inst. Hautes Etudes Sci. Publ. Math., No. 34, 105–112 (1968).

    Google Scholar 

  464. G. Segal, “Categories and cohomology theories,” Topology,13, No. 3, 293–312 (1974).

    Google Scholar 

  465. J.-P. Serre, “Faisceaux algébriques cohérents,” Ann. Math.,61, No. 2, 197–278 (1955).

    Google Scholar 

  466. J.-P. Serre, Modules projectifs et espaces fibrés a fibre vectorielle. Sem. P. Dubreil, Fac. Sci. Paris, 23-1–23-18 (1957–1958).

  467. J.-P. Serre, Sur les modules projectifs. Sem. P. Dubreil, Fac. Sci. Paris, No. 2 (1960–1961).

  468. J.-P. Serre, “Le problème des groupes de congruence pour SL2,” Ann. Math.,92, No. 3, 489–527 (1970).

    Google Scholar 

  469. J.-P. Serre, “Cohomologie des groupes discrets,” Lect. Notes Math.,244, 337–350 (1971).

    Google Scholar 

  470. J.-P. Serre, “Cohomologie des groupes discrets,” Ann. Math. Studies, No. 70, 77–169 (1971).

    Google Scholar 

  471. J. M. Shapiro, “A Riemann-Roch type theorem for the Witt and Milnor rings of a field,” J. Pure Appl. Algebra,15, No. 3, 293–304 (1979).

    Google Scholar 

  472. J. M. Shapiro, “Relations between the Milnor and Quillen K-theory of fields,” J. Pure Appl. Algebra,20, No. 1, 93–102 (1981).

    Google Scholar 

  473. P. K. Sharma and J. R. Strooker, “On a question of Swan in algebraic K-theory,” Ann. Sci. Ecole Norm. Sup.,6, No. 1, 85–94 (1973).

    Google Scholar 

  474. R. W. Sharpe, “On the structure of the unitary Steinberg group,” Ann. Math.,96, No. 3, 444–479 (1972).

    Google Scholar 

  475. R. W. Sharpe, “K2(Z[Z/5])is generated by relations among 2×2 matrices,” Lect. Notes Math.,741, 158–169 (1979).

    Google Scholar 

  476. R. W. Sharpe, “On the structure of the Steinberg group St(Λ),” J. Algebra,68, No. 2, 453–468 (1981).

    Google Scholar 

  477. C. Sherman, “A note on the localization theorem for projective modules,” Proc. Am. Math. Soc.,75, No. 2, 207–208 (1979).

    Google Scholar 

  478. C. C. Sherman, “Some splitting results in the K-theory of rings,” Am. J. Math.,101, No. 3, 609–632 (1979).

    Google Scholar 

  479. C. C. Sherman, “Gersten's conjecture for arithmetic surfaces,” J. Pure Appl. Algebra,14, No. 2, 167–174 (1979).

    Google Scholar 

  480. C. C. Sherman, “The K-theory of an equicharacteristic discrete valuation ring injects into the K-theory of its field of quotients,” Pac. J. Math.,74, No. 2, 497–499 (1978).

    Google Scholar 

  481. C. C. Sherman, “Some theorems on the K-theory of coherent sheaves,” Commun. Algebra,7, No. 14, 1489–1508 (1979).

    Google Scholar 

  482. C. C. Sherman, “K-cohomology of regular schemes,” Commun. Algebra,7, No. 10, 999–1029 (1979).

    Google Scholar 

  483. C. C. Sherman, “K'-theory of Noetherian schemes,” Lect. Notes Math.,854, 343–371 (1981).

    Google Scholar 

  484. J. R. Silvester, “On the K2 of a free associative algebra,” Proc. London Math. Soc.,26, No. 1, 35–56 (1973).

    Google Scholar 

  485. M. K. Siu, “Unitary Whitehead group of cyclic groups,” Bull. Am. Math. Soc.,79, No. 1, 92–95 (1973).

    Google Scholar 

  486. V. Snaith, “On the homology of the general linear groups over Z/4,” Can. J. Math.,30, No. 4, 851–855 (1978).

    Google Scholar 

  487. V. Snaith, “On the localization sequence in K-theory,” Proc. Am. Math. Soc.,79, No. 3, 359–364 (1980).

    Google Scholar 

  488. R. L. Snider, “Is the Brauder group generated by cyclic algebras?,” Lect. Notes Math.,734, 279–301 (1979).

    Google Scholar 

  489. C. Soulé, “Addendum to the article ‘On the torsion in K* Z,’” Duke Math. J.,45, No. 1, 131–132 (1978).

    Google Scholar 

  490. C. Soulé, “The cohomology of SL3(Z),” Topology,17, No. 1, 1–22 (1978).

    Google Scholar 

  491. C. Soulé, “K-theorie de Z et cohomologie etale,” C. R. Acad. Sci. Paris,286, No. 24, A1179-A1181 (1978).

    Google Scholar 

  492. C. Soulé, K-theorie des anneaux d'entiers de corps de nombres et cohomologie etale,” Invent. Math.,55, No. 3, 251–295 (1979).

    Google Scholar 

  493. C. Soulé, “Chevalley Groups over polynomial rings,” London Math. Soc., Lect. Note Ser., No. 36, 359–367 (1979).

    Google Scholar 

  494. C. Soulé, “Rational K-theory of the dual numbers of a ring of algebraic integers,” Lect. Notes Math.,854, 402–408 (1981).

    Google Scholar 

  495. C. Soulé, “On higher p-adic regulators,” Lect. Notes Math.,854, 372–401 (1981).

    Google Scholar 

  496. E. H. Spanier, Algebraic Topology, McGraw-Hill, New York (1966).

    Google Scholar 

  497. T. A. Springer, “A remark on the Milnor ring,” Nederl. Akad. Wetensch. Proc., Ser. A,75, No. 2, 100–102 (1972).

    Google Scholar 

  498. R. E. Staffeldt, “Reduction theory and K3 of the Gaussian integers,” Duke Math. J.,46, No. 4, 773–798 (1979).

    Google Scholar 

  499. J. T. Stafford, “K-theory of Noetherian group rings,” Lect. Notes Math.,734, 302–322 (1979).

    Google Scholar 

  500. J. T. Stafford, “Projective modules over polynomial extensions of division rings,” Invent. Math.,59, No. 2, 105–117 (1980).

    Google Scholar 

  501. J. T. Stafford, “On the stable range of right Noetherian rings,” Bull. London Math. Soc.,13, No. 1, 39–41 (1981).

    Google Scholar 

  502. M. R. Stein, “Relativizing functors on rings and algebraic K-theory,” J. Algebra,19, No. 1, 140–152 (1971).

    Google Scholar 

  503. M. R. Stein, “Surjective stability in dimension 0 for K2 and related functors,” Trans. Am. Math. Soc.,178, 165–191 (1973).

    Google Scholar 

  504. M. R. Stein, “The Schur multipliers of SP6(Z), Spin8(Z), Spin7(Z), and F4(Z),” Math. Ann.,215, No. 2, 165–172 (1975).

    Google Scholar 

  505. M. R. Stein, “Whitehead groups of finite groups,” Bull. Am. Math. Soc.,84, No. 2, 201–212 (1978).

    Google Scholar 

  506. M. R. Stein, “Stability theorems for K1, K2 and related functors modeled on Chevalley Groups,” Jpn. J. Math. (N.S.),4, No. 1, 77–108 (1978).

    Google Scholar 

  507. M. R. Stein, “Excision and K2 of group rings,” J. Pure Appl. Algebra,18, No. 2, 213–224 (1980).

    Google Scholar 

  508. M. R. Stein, “Maps of rings which induce surjections on K3,” J. Pure Appl. Algebra,21, No. 1, 23–49 (1981).

    Google Scholar 

  509. M. R. Stein and R. K. Dennis, “K2 of radical ideals and semilocal rings revisited,” Lect. Notes Math.,342, 281–303 (1973).

    Google Scholar 

  510. M. Steinberger, “On the equivalence of the two definitions of the algebraic K-theory of a topological space,” Lect. Notes Math.,763, 317–331 (1979).

    Google Scholar 

  511. J. Stienstra, “The formal completion of the second Chow group. A K-theoretic approach,” Asterisque, No. 64, 149–168 (1979).

    Google Scholar 

  512. J. Stienstra, “On K2 and K3 of truncated polynomial rings,” Lect. Notes Math.,854, 409–455 (1981).

    Google Scholar 

  513. J. R. Strooker, Le groupe fondamental des groupes linéaires GLn. Sem. P. Dubreil. Algebre. Univ. Pierre et Marie Curie,28, 17/1–17/2 (1974–1975).

    Google Scholar 

  514. J. R. Strooker, “The fundamental group of the general linear group,” J. Algebra,48, No. 2, 477–508 (1977).

    Google Scholar 

  515. J. R. Strooker, “Karoubi-Villamayor K-theory is not homotopy Quillen theory,” Proc. Am. Math. Soc.,73, No. 2, 161–162 (1979).

    Google Scholar 

  516. J. R. Strooker and O. E. Villamayor, “Building K-theories,” Adv. Math.,15, No. 2, 232–268 (1975).

    Google Scholar 

  517. J. R. Strooker and O. E. Villamayor, “A spectral sequence for double complexes of groups,” Adv. Math.,15, No. 2, 216–231 (1975).

    Google Scholar 

  518. A. A. Suslin, “The cancellation problem for projective modules and related topics,” Lect. Notes Math.,734, 323–338 (1979).

    Google Scholar 

  519. A. A. Suslin, “Stability in algebraic K-theory,” Preprint LOMI, No. E-2 (1980).

  520. A. A. Suslin, “Mennicke symbols and their applications in the K-theory of fields,” Preprint LOMI, No. E-2 (1981).

  521. A. A. Suslin, “On the equivalence of K-theories,” Commun. Algebra,9, No. 15, 1559–1566 (1981).

    Google Scholar 

  522. A. A. Suslin, “Homology of GLn characteristic classes and Milnor K-theory,” Zap. Nauch. Sem. LOMI (1982).

  523. A. A. Suslin, “Torsion in K2,” Preprint LOMI (1982).

  524. R. G. Swan, “The number of generators of a module,” Math. Z.,102, No. 4, 318–322 (1967).

    Google Scholar 

  525. R. G. Swan, “Vector bundles and projective modules,” Trans. Am. Math. Soc.,105, No. 2, 264–277 (1962).

    Google Scholar 

  526. R. G. Swan, “Non-Abelian homological algebra and K-theory,” Proc. Sympos. Pure Math.,17, 88–123 (1970).

    Google Scholar 

  527. R. G. Swan, Algebraic K-Theory, Springer-Verlag, Berlin (1968).

    Google Scholar 

  528. R. G. Swan, “Some relations between higher K-functors,” J. Algebra,21, No. 1, 113–136 (1972).

    Google Scholar 

  529. R. G. Swan, “Excision in algebraic K-theory,” J. Pure Appl. Algebra,1, No. 3, 221–252 (1971).

    Google Scholar 

  530. R. G. Swan, Algebraic K-theory. Actes Conr. Int. Math., 1970, Tome 1, Paris (1971), pp. 191–199.

    Google Scholar 

  531. R. G. Swan, “A splitting principle in algebraic K-theory,” Proc. Symp. Pure Math.,21, 153–159 (1971).

    Google Scholar 

  532. R. G. Swan, “K-theory and algebraic correspondences,” Lect. Notes Math.,353, 161–179 (1973).

    Google Scholar 

  533. R. G. Swan, “A cancellation theorem for projective modules in the metastable range,” Invent. Math.,27, Nos. 1–2, 23–43 (1974).

    Google Scholar 

  534. R. G. Swan, “Serre's problem,” Queen's Papers Pure Appl. Math., No. 42, 2–60 (1975).

    Google Scholar 

  535. R. G. Swan, “Topological examples of projective modules,” Trans. Am. Math. Soc.,230, 201–234 (1977).

    Google Scholar 

  536. R. G. Swan, “Projective modules over Laurent polynomial rings,” Trans. Am. Math. Soc.,237, 111–120 (1978).

    Google Scholar 

  537. R. G. Swan (notes by E. Graham Evans), K-Theory of Finite Groups and Orders, Springer-Verlag, Berlin (1970).

    Google Scholar 

  538. R. G. Swan and J. Towber, “A class of projective modules which are nearly free,” J. Algebra,36, No. 3, 427–434 (1975).

    Google Scholar 

  539. J. Tate, Symbols in arithmetic. Actes Congr. Int. Math., 1970, Tome 1, Paris (1971), pp. 201–211.

    Google Scholar 

  540. J. Tate, “Letter from Tate to Iwasawa on a relation between K2 and Galois cohomology,” Lect. Notes Math.,342, 524–527 (1973).

    Google Scholar 

  541. J. Tate, On the torsion in K2 of fields. Algebraic Number Theory. Proc. Taniguchi Internat. Symp. Div. Math., No. 2, Kyoto, 1976, Tokyo (1977), pp. 243–261.

    Google Scholar 

  542. J. Tate, “Relations between K2 and Galois cohomology,” Invent. Math.,36, 257–274 (1976).

    Google Scholar 

  543. Theorie des Intersections et Théorème de Riemann-Roch, Lect. Notes Math.,225, Springer-Verlag, Berlin (1971).

  544. C. B. Thomas, “Characteristic classes of representations over imaginary quadratic fields,” Lect. Notes Math.,788, 471–481 (1980).

    Google Scholar 

  545. R. W. Thomason, “First quadrant spectral sequences in algebraic K-theory,” Lect. Notes Math.,763, 332–355 (1979).

    Google Scholar 

  546. M. Tierney and M. Vogel, “Simplicial resolutions and derived functors,” Math. Z.,111, No. 1, 1–14 (1969).

    Google Scholar 

  547. J.-P. Tignol, “Central simple algebras with involution,” in: Ring Theory (Proc. Antwerp Conf., 1978), Dekker, New York (1979), pp. 279–285.

    Google Scholar 

  548. J. Towber, “Serre's problem on projective modules,” Queen's Papers Pure Appl. Math., No. 41, 25 (1974).

    Google Scholar 

  549. L. N. Vaserstein, “On the normal subgroups of GLn over a ring,” Lect. Notes Math.,854, 456–465 (1981).

    Google Scholar 

  550. P. Vogel, “Localization of algebraic L-theory,” Lect. Notes Math.,788, 482–495 (1980).

    Google Scholar 

  551. K. Vogtmann, “Homology stability for On,n,” Commun. Algebra,7, No. 1, 9–38 (1979).

    Google Scholar 

  552. T. Vorst, “Localization of the K-theory of polynomial extension,” Math. Ann.,244, No. 1, 33–53 (1979).

    Google Scholar 

  553. T. Vorst, “The general linear group of polynomial ring over regular rings,” Commun. Algebra,9, No. 5, 499–509 (1981).

    Google Scholar 

  554. J. B. Wagoner, “On K2 of the Laurent polynomial ring,” Am. J. Math.,93, No. 1, 123–138 (1971). ~

    Google Scholar 

  555. J. B. Wagoner, “Delooping classifying spaces in algebraic K-theory,” Topology,11, No. 4, 349–370 (1972).

    Google Scholar 

  556. J. B. Wagoner, “Buildings, stratifications, and higher K-theory,” Lect. Notes Math.,341, 148–176 (1973).

    Google Scholar 

  557. J. B. Wagoner, “Homotopy theory for the p-adic special linear group,” Comment. Math. Helv.,50, No. 4, 535–559 (1975).

    Google Scholar 

  558. J. B. Wagoner, “Delooping the continuous K-theory of a valuation ring,” Pac. J. Math.,65, No. 2, 533–538 (1976).

    Google Scholar 

  559. J. B. Wagoner, “Stability for homology of the general linear group of a local ring,” Topology,15, No. 4, 417–423 (1976).

    Google Scholar 

  560. J. B. Wagoner, “Continuous cohomology and p-adic K-theory,” Lect. Notes Math.,551, 241–248 (1976).

    Google Scholar 

  561. J. B. Wagoner, “Equivalence of algebraic K-theories,” J. Pure Appl. Algebra,11, Nos.1–3, 245–269 (1977).

    Google Scholar 

  562. F. Waldhause, “Whitehead groups of generalized free products,” Lect. Notes Math.,342, 155–179 (1973).

    Google Scholar 

  563. F. Waldhause, “Algebraic K-theory of generalized free products. I, II,” Ann. Math.,108, No. 1, 135–204; No. 2, 205–256 (1978).

    Google Scholar 

  564. F. A. Waldhausen, “Algebraic K-theory of topological spaces. I,” Proc. Symp. Pure Math.,32, 35–60 (1978).

    Google Scholar 

  565. C. T. C. Wall, “Norms of units in group rings,” Proc. London Math. Soc.,29, No. 4, 593–632 (1974).

    Google Scholar 

  566. C. T. C. Wall, “Equivariant algebraic K-theory,” London Math. Soc. Lect. Note Ser., No. 11, 111–118 (1974).

    Google Scholar 

  567. C. A. Weibel, “The homotopy exact sequence in algebraic K-theory,” Commun. Algebra,6, No. 16, 1635–1646 (1978).

    Google Scholar 

  568. C. A. Weibel, “Nilpotence and K-theory,” J. Algebra,61, No. 2, 298–307 (1979).

    Google Scholar 

  569. C. A. Weibel, “K-theory and analytic isomorphisms,” Invent. Math.,61, No. 2, 177–197 (1980).

    Google Scholar 

  570. C. A. Weibel, “K2, K3 and nilpotent ideals,” J. Pure Appl. Algebra,18, No. 3, 333–345 (1980).

    Google Scholar 

  571. C. A. Weibel, “Mayer-Vietoris sequences and module structures on NK*,” Lect. Notes Math.,854, 466–493 (1981).

    Google Scholar 

  572. C. A. Weibel, “A survey of products in algebraic K-theory,” Lect. Notes Math.,854, 494–517 (1981).

    Google Scholar 

  573. S. M. J. Wilson, “K-theory for twisted group rings,” Proc. London Math. Soc.,29, No. 2, 257–271 (1974).

    Google Scholar 

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Translated from Itogi Nauki i Tekhniki, Seriya Algebra, Topologiya, Geometriya, Vol. 20, pp. 71–152, 1982.

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Suslin, A.A. Algebraic K-theory. J Math Sci 28, 870–923 (1985). https://doi.org/10.1007/BF02105457

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