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Algebraic K-Theory pp 334–356Cite as

Mennicke symbols and their applications in the k-theory of fields

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Literature

  1. D. W. Anderson, Relationship among K-theories, pp. 57–72 of Lecture Notes in Math. no. 341, Springer-Verlag, Berlin and New York, 1973.

    MATH  Google Scholar 

  2. D. W. Anderson, M. Karoubi, and J. Wagoner, Relations between higher K-theories, pp. 73–81 of Lecture Notes in Math. no. 341, Springer-Verlag, Berlin and New York, 1973.

    Book  MATH  Google Scholar 

  3. H. Bass, Algebraic K-Theory, Benjamin, New York, 1968.

    MATH  Google Scholar 

  4. H. Bass and J. Tate, The Milnor ring of a global field, pp. 349–446 of Lecture Notes in Math. no. 342, Springer-Verlag, Berlin and New York, 1973.

    MATH  Google Scholar 

  5. R. Fossum, H. B. Foxby, and B. Iversen, A characteristic class in algebraic K-theory, Aarhus University, preprint no. 29 (1978/79).

    Google Scholar 

  6. S. M. Gersten, Higher K-theory of rings, pp. 3–42 of Lecture Notes in Math. no. 341, Springer-Verlag, Berlin and New York, 1973.

    Book  MATH  Google Scholar 

  7. M. Karoubi, La périodicité de Bott en K-théorie générale, Ann. Sci. École Norm. Sup. (4) 4 (1971), 63–95.

    MathSciNet  MATH  Google Scholar 

  8. M. Karoubi and O. Villamayor, Foncteurs Kn en algèbre et en topologie, C. R. Acad. Sci. Paris Sér. A-B 269 (1969), A416–419.

    MathSciNet  MATH  Google Scholar 

  9. K. Kato, The norm homomorphism of Milnor’s K-group, note passed out at the Oberwolfach K-Theory Conference, appears as §1.7 in "A generalization of local class field theory by using K-groups, II, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 27 (1980), 603–683".

    MathSciNet  Google Scholar 

  10. F. Keune, (t2-t)-Reciprocities on the affine line and Matsumoto’s theorem, Invent. Math. 28 (1975), 185–192.

    Article  MathSciNet  MATH  Google Scholar 

  11. M. I. Krusemeyer, Fundamental groups, algebraic K-theory, and a problem of Abhyankar, Invent. Math. 19 (1973), 15–47.

    Article  MathSciNet  MATH  Google Scholar 

  12. J. Milnor, Introduction to Algebraic K-Theory, Annals of Math. Studies No. 72, Princeton University Press, Princeton, 1971.

    MATH  Google Scholar 

  13. D. Quillen, Higher algebraic K-theory: I, pp. 85–147 of Lecture Notes in Math. no. 341, Springer-Verlag, Berlin and New York, 1973.

    MATH  Google Scholar 

  14. M. Raynaud, Modules projectifs univèrsels, Invent. Math. 6 (1968), 1–26.

    Article  MathSciNet  MATH  Google Scholar 

  15. A. A. Suslin and L. N. Vaserstein, Serre’s problem on projective modules over polynomial rings and algebraic K-theory, Izv. Akad. Nauk SSSR Ser. Mat. 40 (1976), 993–1054 = Math. USSR Izv. 10 (1976), 937–1001.

    MathSciNet  MATH  Google Scholar 

  16. A. A. Suslin, On the structure of the special linear group over a polynomial ring, Izv. Akad. Nauk SSSR Ser. Math. 41, no. 2, (1977), 235–252 = Math. USSR Izv. 11 (1977), 221–238.

    MathSciNet  MATH  Google Scholar 

  17. A. A. Suslin, On stably free modules, Mat. Sb. 102 (144), no. 4, (1977), 537–550.

    MathSciNet  MATH  Google Scholar 

  18. A. A. Suslin, On the cancellation problem for projective modules, preprint LOMI, P-4-77, Leningrad, 1977.

    Google Scholar 

  19. A. A. Suslin, The cancellation problem for projective modules and related topics, pp. 323–338 of Lecture Notes in Math. no. 734, Springer-Verlag, Berlin and New York, 1979.

    MATH  Google Scholar 

  20. A. A. Suslin, Reciprocity laws and stable range in polynomial rings, Izv. Akad. Nauk SSSR 43, no. 6, (1979), 1394–1425.

    MathSciNet  MATH  Google Scholar 

  21. R. G. Swan, A cancellation theorem for projective modules in the metastable range, Invent. Math. 27 (1974), 23–43.

    Article  MathSciNet  MATH  Google Scholar 

  22. R. G. Swan and J. Towber, A class of projective modules which are nearly free, J. Algebra 36 (1975), 427–434.

    Article  MathSciNet  MATH  Google Scholar 

  23. L. N. Vaserstein, On the stabilization of the general linear group over a ring, Mat. Sb. 79(121), no. 3, (1969), 405–424 = Math. USSR Sb. 8 (1969), 383–400.

    MathSciNet  Google Scholar 

  24. L. N. Vaserstein, Stable rank of rings and dimensionality of topological spaces, Funkcional. Anal. i Priložen. 5 (1971), 17–27 = Functional Anal. Appl. 5 (1971), 102–110.

    MathSciNet  MATH  Google Scholar 

  25. C. A. Weibel, A survey of products in algebraic K-theory, pp. 494–517 of Lecture Notes in Math. no. 854, Springer-Verlag, Berlin and New York, 1981.

    MATH  Google Scholar 

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Authors and Affiliations

  1. LOMI, Fontanka 27, Leningrad, USSR

    A. A. Suslin

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  1. A. A. Suslin
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R. Keith Dennis

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© 1982 Springer-Verlag

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Suslin, A.A. (1982). Mennicke symbols and their applications in the k-theory of fields. In: Dennis, R.K. (eds) Algebraic K-Theory. Lecture Notes in Mathematics, vol 966. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062182

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  • DOI: https://doi.org/10.1007/BFb0062182

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  • Print ISBN: 978-3-540-11965-4

  • Online ISBN: 978-3-540-39553-9

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