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Modules

  • Chapter
Algebra and Geometry

Part of the book series: Progress in Mathematics ((PM,volume 12))

Abstract

In the present article we consider the papers on the theory of modules reviewed in the Mathematics section of Referativnyi Zhurnal during 1966–1968. Unless we specify otherwise all the modules to be considered in the survey are taken to be left and and unitary. Therefore, as a rule we shall set forth the left-sided versions of the results regardless of which version was chosen by the author or by the reviewer. When we speak of work which has already been mentioned in previous issues of “Itogi Nauki” (Progress in Mathematics), we shall make reference to these issues.

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Bibliography

  1. V. A. Andrunakievich, V. I. Arnautov, and Yu. M. Ryabukhin, “Rings,”in: R. V. Gamkrelidze (Ed.), Progress in Mathematics, Vol. 5: Algebra, Plenum Press, New York (1969), pp. 127–177.

    Google Scholar 

  2. V. A. Andrunakievich and Yu. M. Ryabukhin, “On the additive theory of ideals in rings, modules, and groupoids,”Dokl. Akad. Nauk SSSR, 168(3):495–498 (1966).

    MathSciNet  Google Scholar 

  3. Z. I. Borevich and D. K. Faddeev, “A remark on orders with a cyclic index,”Dokl. Akad. Nauk SSSR, 164(4):727–728 (1965).

    MathSciNet  Google Scholar 

  4. Z. I. Borevich and D. K. Faddeev, “Representations of orders with a cyclic index,”Tr. Mat. Inst. Akad. Nauk SSSR, 80:51–65 (1965).

    Google Scholar 

  5. B. B. Venkov, “Homological algebra,”in: Algebra, 1964 [in Russian], Science Summaries, VINITI, Akad. Nauk SSSR, Moscow (1966), pp. 203–235.

    Google Scholar 

  6. R. T. Vol’vachev, “Elementary theory of modules,”Vestsi Akad. Nauk BSSR, Ser. Fiz.-Mat. Nauk, No. 4, 7–12 (1967).

    Google Scholar 

  7. V. I. Gemintern, “Semiprimary rings with an atomic structure of left ideals,”Sibirsk. Mat. Zh., 8(4):947–95l (1967).

    MathSciNet  Google Scholar 

  8. L. M. Gluskin, “Endomorphisms of modules,”in: Algebra and Mathematical Logic [in Russian], Kiev Univ., Kiev (1966), pp. 3–20.

    Google Scholar 

  9. V. E. Govorov, “Derived radicals of modules,”Mat. Zametki, 3(6):633–642 (1968).

    MathSciNet  MATH  Google Scholar 

  10. E. L. Gorbachuk, “Splittability of torsion and pretorsion in the category of right -modules,”Mat. Zametki, 2(6):681–688 (1967).

    MathSciNet  MATH  Google Scholar 

  11. P. M. Gudivok, “Representations of finite groups over number rings,”Izv. Akad. Nauk SSSR, Ser. Mat., 31(4):799–834 (1967).

    MathSciNet  Google Scholar 

  12. Yu. A. Drozd and V. V. Kirichenko, “Hereditary orders,”Ukrainsk. Mat. Zh., 20(2):246–248 (1968).

    MATH  Google Scholar 

  13. Yu. A. Drozd, V. V. Kirichenko, and A. V. Roiter, “Hereditary and Bass orders,”Izv. Akad. Nauk SSSR, Ser. Mat., 31:1415–1436 (1967).

    MathSciNet  MATH  Google Scholar 

  14. Yu. A. Drozd and A. V. Roiter, “Commutative rings with a finite number of indecomposable integral representations,”Izv. Akad. Nauk SSSR, Ser. Mat., 31(4):783–798 (1967).

    MathSciNet  MATH  Google Scholar 

  15. Yu. A. Drozd and V. M. Turchin, “The number of modules of representations in genus for second-order integral matrix rings,”Mat. Zametki, 2(2):133–138 (1967).

    MathSciNet  MATH  Google Scholar 

  16. V. P. Elizarov, “Nonsingularly dimensional rings,”Sibirsk. Mat. Zh., 6(5):1181–1184 (1965).

    MathSciNet  MATH  Google Scholar 

  17. V. P. Elizarov, “Quotient modules,”Sibirstk. Mat. Zh., 7(1):221–226 (1966).

    MathSciNet  MATH  Google Scholar 

  18. V. P. Elizarov, “Flat extensions of rings,”Dokl. Akad. Nauk SSSR, 175(4):759–761 (1967).

    MathSciNet  Google Scholar 

  19. M. Kol’p, “Growth rings,”Sibirsk. Mat. Zh., 8(5):1193–1196 (1967).

    Google Scholar 

  20. V. V. Kirichenko, “Orders all of whose representations are completely decomposable,”Mat. Zametki, 2(2):139–144 (1967).

    MathSciNet  Google Scholar 

  21. L. A. Coifman, “A radical of a module,”Sibirsk. Mat. Zh., 7(5):1204–1207 (1966).

    Google Scholar 

  22. V. I. Kuz’minov, “Derived functors of a projective limit,”Sibirsk. Mat. Zh., 8(2):333–345 (1967).

    MathSciNet  MATH  Google Scholar 

  23. C. W. Curtis and I. Reiner, Theory of Representations of Finite Groups and of Associative Algebras [Russian translation], Nauka, Moscow (1969), 668 pp.

    Google Scholar 

  24. E. M. Levich, “Modules over the ring of polynomials in one endomorphism,”Latvian Math. Annual, Vol. 2 [in Russian], Riga (1966), pp. 127–174.

    MATH  Google Scholar 

  25. S. A. Lang, Algebra [Russian translation], “Mir,”Moscow (1968), 564 pp.

    MATH  Google Scholar 

  26. S. MacLane, Homology [Russian translation], “Mir,”Moscow (1966), 543 pp.

    MATH  Google Scholar 

  27. A. P. Mishina and L. A. Skornyakov, Abelian Groups and Modules [in Russian], “Nauka,”Moscow (1969), 151 pp.

    MATH  Google Scholar 

  28. A. V. Mikhalev, “Isomorphisms of endomorphism semigroups of modules,”Algebra i Logika. Seminar, 5(5):59–67 (1966).

    MATH  Google Scholar 

  29. A. V. Mikhalev, “Isomorphisms of endomorphism semigroups of modules. II,”Algebra i Lokika. Seminar, 6(2):35–47 (1967).

    MathSciNet  MATH  Google Scholar 

  30. L. A. Nazarova and A. V. Roiter, “Refinement of a theorem of Bass,”Dokl. Akad. Nauk SSSR, 176(2):266–268 (1967).

    MathSciNet  Google Scholar 

  31. B. I. Plotkin, “Certain aspects of the general theory of group representations,” Izv. Akad. Nauk SSSR, Ser. Mat., 27(4):855–882 (1963).

    MathSciNet  MATH  Google Scholar 

  32. I. S. Ponizovskii, “The Frobeniusness of the semigroup algebra of a finite commutative semigroup,” Izv. Akad. Nauk SSSR, Ser. Mat., 32(4):820–836 (1968).

    MathSciNet  Google Scholar 

  33. A. V. Roiter, “Analog of a theorem by Bass for the modules of representations of noncommutative orders,” Dokl. Akad. Nauk SSSR, 168(6):1261–1264 (1966).

    MathSciNet  Google Scholar 

  34. A. V. Roiter, “Integral representations belonging to one genus,” Izv. Akad. Nauk SSSR, Ser. Mat., 30(6):1315–1324 (1966).

    MathSciNet  Google Scholar 

  35. B. M. Rudyk, “Extensions of modules,” Dokl. Akad. Nauk SSSR, 179(3):545–547 (1968).

    MathSciNet  Google Scholar 

  36. Yu. M. Ryabukhin, “Radicals in categories,” in: Mathematical Researches, Vol. 2, No. 3 [in Russian], Kishinev (1967), pp. 107–165.

    MATH  Google Scholar 

  37. I. I. Sakhaev, “Exactness of functors,” Izv. Vyssh. Uchebn. Zavedenii. Matematika, No. 4, 104–108 (1966).

    Google Scholar 

  38. J.-P. Serre, “Local algebra and the theory of multiplicities,” Period. Sb. Perev. Statei, 7(5):3–93 (1963).

    Google Scholar 

  39. L. A. Skornyakov, “Rings,” in: Algebra. Topology. 1962 [in Russian], Science Summaries, VINITI, Akad. Nauk SSSR, Moscow (1963), pp. 59–79.

    Google Scholar 

  40. L. A. Skornyakov, “Modules,” in: Algebra. Topology. 1962 [in Russian], Science Summaries, VINITI, Akad. Nauk SSSR, Moscow (1963), pp. 80–89.

    Google Scholar 

  41. L. A. Skornyakov, “Cohn rings,” Algebra i Logika. Seminar, 4(3):5–30 (1965).

    MATH  Google Scholar 

  42. L. A. Skornyakov, “Modules,” in: R. V. Gamkrelidze (Ed.), Progress in Mathematics. Vol. 5: Algebra, Plenum Press, New York - London (1969), pp. 179–214.

    Google Scholar 

  43. L. A. Skornyakov, “Elizarov quotient ring and the localization principle,” Mat. Zametki, 1(3):263–268 (1967).

    MathSciNet  MATH  Google Scholar 

  44. L. A. Skornyakov, “Lectures on homological algebra,” Mat. Vesn., 5(1):71–113 (1968).

    Google Scholar 

  45. L. A. Skornyakov, “Homological classification of rings,” Mat. Vesn., 4(4):415–434 (1967).

    Google Scholar 

  46. T. S. Tol’skaya, “Injection and freedom,” Sibirsk. Mat. Zh., 6(5):1202–1207 (1965).

    MATH  Google Scholar 

  47. D. K. Faddeev, “Introduction to the multiplicative theory of modules of integral representations,” Tr. Mat. Inst. Akad. Nauk SSSR, 80:145–182 (1965).

    MathSciNet  MATH  Google Scholar 

  48. D. K. Faddeev, “On the theory of cubic Z-rings,” Tr. Mat. Inst. Akad. Nauk SSSR, 80:183–187 (1965).

    MathSciNet  MATH  Google Scholar 

  49. V. G. Fayans, “Endomorphisms of ordered linear spaces,” Herzen Lectures, XIX, Math. [in Russian], Leningrad. Gos. Ped. Inst., Leningrad (1966), pp. 10–12.

    Google Scholar 

  50. V. G. Fayans, “Endomorphism semigroups of ordered linear spaces,” Uch. Zap. Leningrad. Gos. Ped. Inst. im. A. I. Gertsen [Herzen], 302:124–141 (1967).

    Google Scholar 

  51. G. M. Tsukerman, “Endomorphism rings of free modules,” Sibirsk. Mat. Zh., 7(5):1161–1167 (1966).

    Google Scholar 

  52. T. Akiba, Remarks on generalized rings of quotients. Proc. Japan Acad., 40(10): 801–806 (1964).

    MathSciNet  MATH  Google Scholar 

  53. T. Akiba, Remarks on generalized rings of quotients. II. J. Math. Kyoto Univ., 5 (1):39–44 (1965).

    MathSciNet  MATH  Google Scholar 

  54. J. S. Alin, “Structure of torsion modules,” Doctoral dissertation, Univ. of Nebraska, (1967), 59 pp.; Dissert. Abstr., B28(7):2925–2926 (1968).

    Google Scholar 

  55. J. S. Alin and S. E. Dickson, Goldie’s torsion theory and its derived functor. Pacif. J. Math., 24(2):195–203 (1968).

    MathSciNet  MATH  Google Scholar 

  56. A. P. Andrews, Modules over a one-dimensional Noetherian ring. Quart. J. Math., 18(69):65–80 (1967).

    MATH  Google Scholar 

  57. J. T. Arnold and R. Gilmer, Idempotent ideals and unions of nets of Prüfer do mains. J. Sci. Hiroshima Univ., Ser. A, Div. 1, 31(2):131–145 (1967).

    MathSciNet  MATH  Google Scholar 

  58. M. Auslander, Remarks on a theorem of Bourbaki, Nagoya Math. J., 27 (1):361–369 (1966).

    MathSciNet  MATH  Google Scholar 

  59. G. Azumaya, Completely faithful modules and self-injective rings. Nagoya Math. J., 27(2):697–708 (1966).

    MathSciNet  MATH  Google Scholar 

  60. A. C. Baker, Systems of linear equations over a topological module. Quart. J. Math., 15(60):327–336 (1964).

    MATH  Google Scholar 

  61. S. Balcerzyk, The global dimension of the group rings of Abelian groups. Fundam. math., 55(3):293–301 (1964).

    MathSciNet  Google Scholar 

  62. S. Balcerzyk, The global dimension of the group rings of Abelian groups. II. Fundam. math., 58(1):67–73 (1966).

    MathSciNet  MATH  Google Scholar 

  63. S. Balcerzyk, On projective dimension of direct limit of modules. Bull. Acad. Polon. sci. Sér. math., astron. et phys., 14(5):241–244 (1966).

    MathSciNet  MATH  Google Scholar 

  64. S. Balcerzyk, On functors and Hom . Bull. Acad. polon. sci. Sér. sci. math., astron. et phys., 15(4):235–238 (1967).

    MathSciNet  MATH  Google Scholar 

  65. B. Ballet, Idéaux maximaux associés a un module artinien. C. r. Acad. sci., 263(21):A758–A76l (1966).

    MathSciNet  Google Scholar 

  66. B. Ballet, Structure des modules artiniens (cas commutatif). C. r. Acad. sci., 266(1):A1–A4 (1968).

    MathSciNet  Google Scholar 

  67. B. Banaschewski, On coverings of modules. Math. Nachr., 31(1–2):57–71 (1966).

    MathSciNet  MATH  Google Scholar 

  68. B. Banaschewski, On the injective hulls of cyclic modules over Dedekind domains. Canad. Math. Bull., 9(2):183–186 (1966).

    MathSciNet  MATH  Google Scholar 

  69. H. Bass, Finistic dimensions and a homological generalisation of semi-primary rings. Trans. Amer. Math. Soc. 95(3):466–488 (1960).

    MathSciNet  MATH  Google Scholar 

  70. H. Bass, Torsion free and projective modules. Trans. Amer. Math. Soc., 102(2): 319–327 (1962).

    MathSciNet  MATH  Google Scholar 

  71. H. Bass, On the ubiquity of Gorenstein rings. Math. Z., 82 (1):8–28 (1963).

    MathSciNet  MATH  Google Scholar 

  72. H. Bass, Anneaux de Gorenstein. Sémin. Dubreil et Pisot. Fac. Sci. Paris, 16(1): 5/01–5/08 (1967).

    MathSciNet  Google Scholar 

  73. K. Baumgartner, Bemerkungen zum Isomorphieproblem der Ringe. Monatsh.

    Google Scholar 

  74. H. B. Beckwith, “On trace for modules with applications to algebras,” Doctoral. dissertation, Univ. California, San Diego (1967), 68 pp.; Dissert. Abstr., B28(7): 2926 (1968).

    Google Scholar 

  75. J. C. Beidleman, A radical for near-ring modules. Mich. Math. J., l2(3):377–383 (1965).

    MathSciNet  MATH  Google Scholar 

  76. J. D. Beidleman, “On near-rings and near-ring modules,” Doctoral, dissertation., Pennsylvania State Univ. (1964), 178 pp.; Dissert. Abstr., 25(8):4616–4617 (1965).

    Google Scholar 

  77. J. C. Beidleman, Strictly prime distributívely generated near-rings. Math. Z., 100(2):97–105 (1967).

    MathSciNet  MATH  Google Scholar 

  78. P. R. Bongale, Filtered Frobenius algebras. Math. Z., 97(4):320–325 (1967).

    MathSciNet  MATH  Google Scholar 

  79. P. R. Bongale, Filtered Frobenius algebras. II. J. Algebra, 9 (1):79–93 (1968).

    MathSciNet  MATH  Google Scholar 

  80. P. R. Bongale, Filtered Quasi-Frobenius rings. Math. Z., 106(3):191–196 (1968).

    MathSciNet  MATH  Google Scholar 

  81. M.-P. Brameret, “Largeurs d’anneaux et de modules,” Doctoral dissertation, Univ. Paris (1965), 106 pp.

    Google Scholar 

  82. J. Brandenburg, “Über die Rechtsderivierten des inversen Limes von Modul- und Gruppenfamilien,” Doctoral dissertation, Friedrich Wilhelms-Univ., Bonn; Bonn math. Schr., Vol. 11, No. 27 (1967), 65 pp.

    MATH  Google Scholar 

  83. J. O. Brooks, “Classification of representation modules over quadratic orders,” Doctoral dissertation, Univ. Michigan (1964), 64 pp.; Dissert. Abstr., 25(2, Part l):7287–7288 (1965).

    Google Scholar 

  84. A. Brumer, Pseudocompact algebras, profinite groups and class formations. J. Algebra, 4(3):442–470 (1966).

    MathSciNet  MATH  Google Scholar 

  85. A. Brumer, Pseudocompact algebras, profinite groups and class formation. Bull. Amer. Math. Soc., 72(2):321–324 (1966).

    MathSciNet  MATH  Google Scholar 

  86. D. A. Buchsbaum, A note on homology in categories. Ann. Math., 69(1):66–74 (1959).

    MathSciNet  MATH  Google Scholar 

  87. L. Budach, Zum Begriff des Mod-ulquotienten. Monatsber. Dtsch. Akad. Wiss. Berlin, 6(2):81–85 (1964).

    MathSciNet  MATH  Google Scholar 

  88. R. T. Bumby, Modules which are isomorphic to submodules of each other. Arch. Math., 16(3):184–185 (1965).

    MathSciNet  MATH  Google Scholar 

  89. L. Burch, A note on ideals of homological dimension one in local domains. Proc. Cambridge Philos. Soc., 63(3):661–662 (1967).

    MathSciNet  MATH  Google Scholar 

  90. M. C. R. Butler, Torsion-free modules and diagrams of vector spaces. Proc. London Math. Soc., 18(4):635–652 (1968).

    MathSciNet  MATH  Google Scholar 

  91. M. C. R. Butler and G. Horrocks, Classes of extensions and resolutions. Phil. Trans. Royal. Soc. London, 254:155–202 (1961).

    MathSciNet  MATH  Google Scholar 

  92. H. S. Butts and W. Smith, Prüfer rings. Math. Z., 95(3):196–211 (1967).

    MathSciNet  MATH  Google Scholar 

  93. H. S. Butts and L. I. Wade, Two criteria for Dedekind domains. Amer. Math. Monthly, 73(1):14–21 (1966).

    MathSciNet  MATH  Google Scholar 

  94. W. H. Caldwell, “Rings for which cyclic modules have cyclic injective hulls,” Doctoral Dissertion, Rutgers State Univ. (1966), 60 pp.; Dissert. Abstrs., B27(6):2015 (1966).

    Google Scholar 

  95. W. H. Caldwell, Hypercyclic rings. Pacif. J. Math., 24 (1):29–44 (1968).

    MathSciNet  MATH  Google Scholar 

  96. D. W. Cassel, “Rings over which projective modules are free,” Doctoral dissertation, Syracuse Univ. (1967), 81 pp.; Dissert. Abstr., B28(4):1607–1608 (1967).

    Google Scholar 

  97. J.-Y. Chamard, Modules riches en co-irréductibles et sousmodules compléments. C. r. Acad. sci., 264(23):A987–A990 (1967).

    MathSciNet  Google Scholar 

  98. R. E. Chandler and K. Koh, Applications of a function topology on rings with unit. Ill. J. Math. 11(4):580–585 (1967).

    MathSciNet  MATH  Google Scholar 

  99. N. Chaptal, Sur les modules quasi-injectifs. C. R. acad. sci., 264(4):A173–A175 (1966).

    MathSciNet  Google Scholar 

  100. A.Charnow, Extension of the ground fields in a k[X1, ...,Xn] module. J. London Math. Soc., 41(3):425–432 (1966).

    MathSciNet  MATH  Google Scholar 

  101. S. U. Chase, Direct products of modules. Trans. Amer. Math. Soc., 97(3):457–473 (1960).

    MathSciNet  Google Scholar 

  102. K.-L. Chew, “Extensions of rings and modules,” Doctoral dissertation, Univ. Brit. Columbia (1965), 129 pp.; Dissert. Abstr., 26(8):4681 (1966).

    Google Scholar 

  103. B.-S. Chwe, Relative homological algebra and homological dimension of Lie algebras. Trans. Amer. Math. Soc., 117(5):477–493 (1965).

    MathSciNet  MATH  Google Scholar 

  104. W. E. Clark, Algebras of global dimension one with a finite ideal lattice. Pacif. J. Math., 23(3):463–471 (1967).

    MATH  Google Scholar 

  105. W. E. Clark, A note on semiprimary PP-rings. Osaka J. Math., 4(1):177–178 (1967).

    MathSciNet  MATH  Google Scholar 

  106. P. M. Cohn, On the free product of associative rings. Math. Z., 71(4):380–398 (1959).

    MathSciNet  MATH  Google Scholar 

  107. P. M. Cohn, Factorization in non-commutative power series rings. Proc. Cambridge Philos. Soc., 58(3):452–464 (1962).

    MathSciNet  MATH  Google Scholar 

  108. P. M. Cohn, Free ideal rings. J. Algebra, 1(1):47–49 (1964).

    MATH  Google Scholar 

  109. P. M. Cohn, Sur une classe d’anneaux héréditaires. Sémin. Dubreil et Pisot. Fac Sci. Paris, 19 (1):7/01–7/05 (1967).

    Google Scholar 

  110. P. M. Cohn, A remark on matrix rings over free ideal rings. Proc. Cambridge Philos. Soc., 62 (1):1–4 (1966).

    MathSciNet  MATH  Google Scholar 

  111. P. M. Cohn, Hereditary local rings. Nagoya Math. J., 27 (1):223–230 (1966).

    MathSciNet  MATH  Google Scholar 

  112. P. M. Cohn, Some remarks on the invariant basis property. Topology, 5(3):215–228 (1966).

    MathSciNet  MATH  Google Scholar 

  113. P. M. Cohn, On the free product of associative rings. III. J. Algebra, 8(3):376–383 (1968).

    MathSciNet  MATH  Google Scholar 

  114. R. R. Colby, “On indecomposable modules over rings with minimum condition,” Doctoral dissertation, Univ. of Washington (1965), 55 pp.; Dissert. Abstr., 26(2): 1059 (1965).

    Google Scholar 

  115. R. R. Colby, On indecomposable modules over rings with minimum condition. Pacif. J. Math., 19 (1):23–33 (1966).

    MathSciNet  MATH  Google Scholar 

  116. R. R. Colby and E. A. Rutter, Semi-primary QF-3 rings. Nagoya Math. J., 32:253–258 (June, 1968).

    MathSciNet  MATH  Google Scholar 

  117. R. C. Courter, The maximal co-rational extension by a module. Canad. J. Math., l8(5):953–962 (1966).

    MathSciNet  MATH  Google Scholar 

  118. J. Dauns, Chains of modules with completely reducible quotients. Pacif. J. Math., 17(2):235–242 (1966).

    MathSciNet  MATH  Google Scholar 

  119. F. R. DeMeyer, The trace map and separable algebras. Osaka J. Math., 3(1):7–11 (1966).

    MathSciNet  MATH  Google Scholar 

  120. R. Desq, Sous-modules isotypiques et sous-modules tertiaires d’un module. Sémin. Dubreil et Pisot. Fac. Sci. Paris, 17(2):25/01–25/l3 (1967).

    Google Scholar 

  121. S. E. Dickson, Decomposition of modules. I. Classical rings. Math. Z., 90(1): 9–13 (1965).

    MATH  Google Scholar 

  122. S. E. Dickson, A torsion theory for Abelian categories. Trans. Amer. Math. Soc., 121(1):223–235 (1966).

    MathSciNet  MATH  Google Scholar 

  123. S. E. Dickson, Noetherian splitting rings are Artinian. J. London Math. Soc., 42(4):732–736 (1967).

    MathSciNet  MATH  Google Scholar 

  124. S. E. Dickson, Decomposition of modules. II. Rings without chain conditions. Math. Z., 104(5):349–357 (1968).

    MathSciNet  MATH  Google Scholar 

  125. S. E. Dickson, Direct Decomposition of Radicals, Proc. Conf. Categorical Algebra, La Jolla, Calif., 1965, Springer, New York (1966), pp. 366–374.

    Google Scholar 

  126. V. Dlab, On the dependence relation over modules (Prelim, commun.), Comment. math. Univ. Carolinae, 6(1):115–117 (1965).

    MathSciNet  MATH  Google Scholar 

  127. V. Dlab, Dependence over modules. Czech. Math. J., 16(1):137–157 (1966).

    MathSciNet  Google Scholar 

  128. V. Dlab, The concept of rank and some related questions in the theory of modules. Comment. Math. Univ. Carolinae, 8(1):39–47 (1967).

    MathSciNet  MATH  Google Scholar 

  129. S. Eilenberg and J. C. Moore, Foundations of relative homological algebra. Mem. Amer. Math. Soc., No. 55 (1965), 39 pp.

    MathSciNet  Google Scholar 

  130. G. Eisenreich, Eine Dualitätsbeziehung zwischen S-Moduln. Math. Nachr., 34(5–6):351–359 (1967).

    MathSciNet  MATH  Google Scholar 

  131. S. Endo, Projective modules over polynomial rings. J. Math. Soc. Japan, 15(3): 339–352 (1963).

    MathSciNet  MATH  Google Scholar 

  132. S. Endo, Completely faithful modules and quasi-Frobenius algebras. J. Math. Soc. Japan, 19(4):437–456 (1967).

    MathSciNet  MATH  Google Scholar 

  133. S. Endo and Y. Watanabe, On separable algebras over a commutative ring. Osaka J. Math., 4(2):233–242 (1967).

    MathSciNet  MATH  Google Scholar 

  134. C. Faith, Rings with ascending condition on annihilators. Nagoya Math. J., 27(1):179–191 (1966).

    MathSciNet  MATH  Google Scholar 

  135. C. Faith, On Köthe rings. Math. Ann., 164(3):207–212 (1966).

    MathSciNet  MATH  Google Scholar 

  136. C. Faith, A general Wedderburn theorem. Bull. Amer. Math. Soc., 73 (1):65–67 (1967).

    MathSciNet  MATH  Google Scholar 

  137. C. Faith, Lectures on Injective Modules and Quotient Rings (1967).

    MATH  Google Scholar 

  138. C. Faith and E. A. Walker, Direct-sum representations of injective modules. J. Algebra, 5(2):203–221 (1967).

    MathSciNet  MATH  Google Scholar 

  139. E. H. Feller, A type of quasi-Frobeni us ring. Canad. Math. Bull., 10(1):19–27 (1967).

    MathSciNet  MATH  Google Scholar 

  140. E. H. Feller and E. W. Swokowski, Prime modules. Canad. J. Math., 17(6):1041–1052 (1965).

    MathSciNet  MATH  Google Scholar 

  141. E. H. Feller and E. W. Swokowski, Semi-prime modules. Canad. J. Math., 18(4): 823–831 (1966).

    MathSciNet  MATH  Google Scholar 

  142. D. Ferrand, Sur les modules qui sont limite projective de leurs localisés. C. r. Acad. sci., AB262(11):A609–A611 (1966).

    MathSciNet  Google Scholar 

  143. D. Ferrand, Epimorphismes d’anneaux et algebres séparables. C. r. Acad. sci., 265(15):A411–A414 (1967).

    MathSciNet  Google Scholar 

  144. M. Flamant, Indice d’une forme quadratique définie sur un module projectif de rang fini sur un anneau de Dedekind. C. r. Acad. sci., 261 (18):3513–3515 (1965).

    MathSciNet  MATH  Google Scholar 

  145. I. Fleischer, A new construction of the injective hull. Canad. Math. Bull., 11(1): 19–21 (1968).

    MathSciNet  MATH  Google Scholar 

  146. J. Fort, Contribution a l’étude des éléments tertiaires et isotypiques dans les modules et les L-algebres. Bull. Soc. math. France, Vol. 92, no. 1, suppl., 99 pp. (1964).

    MathSciNet  Google Scholar 

  147. J. Fort, Sommes directes de sous-modules co-irreductibles d’un module. C. r. Acad. sci., A262(22):1239–1242 (1966).

    MathSciNet  Google Scholar 

  148. J. Forth, Sommes directes de sous-modules co-irréductibles d’un module. Math. Z., 103(5):363–388 (1968).

    MathSciNet  Google Scholar 

  149. P. Freyd, Abelian Categories. An Introduction to the Theory of Functors, Harper, New York (1964), 164 pp.

    MATH  Google Scholar 

  150. A. Fröhlich, Invariants for modules over commutative separable orders. Quart. J. Math., 16(63):193–232 (1965).

    MATH  Google Scholar 

  151. K. R. Fuller, “On the structure of QF-2 and QF-3 rings,” Doctoral dissertation Univ. Oregon (1967), 85 pp.; Dissert. Abstr., B28(6):2518 (1967).

    Google Scholar 

  152. P. Gabriel and U. Oberst, Spectralkategorien und reguläre Ringe in von-Neumann-schen Sinn. Math. Z., 92:389–395 (1966).

    MathSciNet  MATH  Google Scholar 

  153. A. Gailleau, Anneau associé a un module injectif riche en co-irréductibles. C. r. Acad. sci., 264(24):A1040–A1042 (1967).

    Google Scholar 

  154. A. Gailleau, Anneau associé a un module injectif riche en co-irréductibles. Sémin. Dubreil et Pisot. Fac. sci. Paris, 20(2):19/01–19/l0 (1968).

    Google Scholar 

  155. E. R. Gentile, Homomorphismes et fermeture algebrique des modules a coefficients dans un anneau associatif. Publs. Fac. cienc. fisicomat. Univ. nac. La Plata, No. 213, pp. 191–200 (1966).

    Google Scholar 

  156. E. R. Gentile, A uniqueness theorem on rings of matrices. J. Algebra, 6(1):l31–134 (1967).

    MathSciNet  MATH  Google Scholar 

  157. E. R. Gentile, A note on the uniqueness of the invariant factors. Rev. Union mat. argent, y Aroc. fis. argent., 23 (1):31–34 (1966).

    MathSciNet  MATH  Google Scholar 

  158. L. Gewirtzman, Anti-isomorphisms of the endomorphism rings of torsion-free modules. Math. Z., 98(5):391–400 (1967).

    MathSciNet  MATH  Google Scholar 

  159. Y. Give’on, Categories of semimodules: the categorical structural properties of transition systems. Math. Syst. Theor., 1967, 1(1):67–78 (1967).

    MathSciNet  MATH  Google Scholar 

  160. A. W. Goldie, Localization in non-commutative Noetherian rings. J. Algebra, 5(1):89–105 (1967).

    MathSciNet  MATH  Google Scholar 

  161. A. W. Goldie, A note on non-commutative localization. J. Algebra, 8 (1):41–44 (1968).

    MathSciNet  MATH  Google Scholar 

  162. N. S. Gopalakrishnan and R. Sridharan, Homological dimension of Ore-extensions. Pacif. J. Math., 19 (1):67–75 (1966).

    MathSciNet  MATH  Google Scholar 

  163. L. Gouyon, Sur le choix de certaines “P-compacités”. C. r. Acad. sci., 263(10): A345–A347 (1966).

    MathSciNet  Google Scholar 

  164. L. Gouyon, Sur le choix de quelques topologies sur un espace vectoriel ou un module. Ann. Fac. sci. Univ. Toulouse sci. math. et sci. phys., 29:17–34 (1965).

    Google Scholar 

  165. J. Guerindon, Sur lafonction caractéristique d’un module gradué. Bol. Soc. mat. Sao Paulo, 16(1–2):115–127 (1965).

    MathSciNet  Google Scholar 

  166. J. Guerindon, Quelques applications des modules gradues. Sémin. Dubreil et Pisot. Fac. Sci. Paris., 17 (1):4/01–4/11 (1967).

    Google Scholar 

  167. R. M. Hamsher, Commutative, noetherian rings over which every module has a maximal submodule. Proc. Amer. Math. Soc., 17(6):1471–1472 (1966).

    MathSciNet  MATH  Google Scholar 

  168. R. M. Hansher, Commutative rings over which every module has a maximal submodule. Proc. Amer. Math. Soc., 18(6):1133–1137 (1967).

    MathSciNet  Google Scholar 

  169. A. Hanna, Dualität in Moduln. J. reine und angew. Math., 224:113–117 (1966): correction, ibid., 228:220 (1967).

    MathSciNet  MATH  Google Scholar 

  170. M. Harada, Multiplicative ideal theory in hereditary orders. J. Math. Osaka City Univ., 14(2):83–106 (1963).

    MathSciNet  Google Scholar 

  171. M. Harada, Hereditary orders which are dual. J. Math. Osaka City Univ., 14(2): 107–115 (1963).

    MathSciNet  Google Scholar 

  172. M. Harada, On semi-primary PP-rings. Osaka J. Math., 2(1):153–161 (1965).

    MathSciNet  MATH  Google Scholar 

  173. M. Harada, Note on quasi-injective modules. Osaka J. Math., 2(2):351–356 (1965).

    MathSciNet  MATH  Google Scholar 

  174. M. Harada, QF-3 and semi-primary PP-rings. I. Osaka J. Math., 2(2):357–368 (1965).

    MATH  Google Scholar 

  175. M. Harada, QF-3 and semi-primary PP-rings. II. Osaka J. Math., 3(1):21–27 (1966).

    MathSciNet  MATH  Google Scholar 

  176. M. Harada, Hereditary semi-primary rings and triangular matrix rings. Nagoya Math. J., 27(2):463–484 (1966).

    MathSciNet  MATH  Google Scholar 

  177. M. Harada, Note on orders over which an hereditary order is projective. Osaka J. Math., 4(1):151–156 (1967).

    MathSciNet  MATH  Google Scholar 

  178. T. Harase, Adjoint pairs of functors on abelian categories. J. Fac. Sci., Univ. Tokyo, Sec. 1, 13(2):175–182 (1966).

    MathSciNet  MATH  Google Scholar 

  179. M. E. Harris, Some results on coherent rings. Proc. Amer. Math. Soc., 17(2): 474–479 (1966).

    MathSciNet  MATH  Google Scholar 

  180. R. Hart, Endomorphisms of modules over semi-prime rings. J. Algebra, 4 (1):46–51 (1966).

    MathSciNet  MATH  Google Scholar 

  181. R. Hart, Simple rings with uniform right ideals. J. London Math. Soc., 42(4): 614–617 (1967).

    MathSciNet  MATH  Google Scholar 

  182. R. E. Harte, A theorem of isomorphism. Proc. London Math. Soc., l6(4):753–765 (1966).

    MathSciNet  MATH  Google Scholar 

  183. A. Hattori, Rank element of a projective module. Nagoya Math. J., 25:113–125 (March, 1965).

    MathSciNet  MATH  Google Scholar 

  184. A. Hattori, Simple algebras over a commutative ring. Nagoya Math. J., 27(2): 611–616 (1966).

    MathSciNet  MATH  Google Scholar 

  185. A. Heller, Homological algebra in Abelian categories. Ann. Math., 68(3):484–525 (1958).

    MathSciNet  MATH  Google Scholar 

  186. A. Heller, Homological functors. Math. Z., 87(2):283–298 (1965).

    MathSciNet  MATH  Google Scholar 

  187. G. A. Heizer, “On divisibility and injectivity,” Doctoral dissertation, Northwestern Univ. (1964), 70 pp.; Dissert. Abstr., 25(11):6656–6657 (1965).

    Google Scholar 

  188. G. A. Heizer, On divisibility and injectivity. Canad. J. Math., 18(5):901–919 (1966).

    MathSciNet  Google Scholar 

  189. G. Hochschild, Relative homological algebra. Trans. Amer. Math. Soc., 82(1): 246–269 (1956).

    MathSciNet  MATH  Google Scholar 

  190. G. Horrocks, Projective modules over an extension of a local ring. Proc. London Math. Soc., 14(56):714–718 (1964).

    MathSciNet  MATH  Google Scholar 

  191. G. Horrocks, Vector bundles on the punctured spectrum of a local ring. Proc. London Math. Soc., 14(56):689–713 (1964).

    MathSciNet  MATH  Google Scholar 

  192. G. Horrocks, An application of projective homotopy theory to reduction of base. Proc. London Math. Soc., 16(1):40–52 (1966).

    MathSciNet  MATH  Google Scholar 

  193. T. Ishikawa, On injective modules and flat modules. J. Math. Soc. Japan, 17(3): 291–296 (1965).

    MathSciNet  MATH  Google Scholar 

  194. B. Iversen, On flat extension of Noetherian rings. Proc. Amer. Math. Soc., 16(6): 1401–1406 (1965).

    MathSciNet  MATH  Google Scholar 

  195. H. Jacobiski, Sur lesardres commutatifs avec un nombre fini de réseaux indécomposables. Acta math., 118(1–2):1–31 (1967).

    MathSciNet  Google Scholar 

  196. J. P. Jans, Projective injective modules. Pacif. J. Math., 9(4):1103–1108 (1959).

    MathSciNet  MATH  Google Scholar 

  197. J. P. Jans, Rings and Homology, Holt, Rinehart and Winston, New York (1964), 88 pp.

    Google Scholar 

  198. J. P. Jans, Some aspects of torsion. Pacif. J. Math., 15(4):1249–1259 (1965).

    MathSciNet  MATH  Google Scholar 

  199. J. P. Jans, On orders in quasi-Frobenius rings. J. Algebra, 7 (1):35–43 (1967).

    MathSciNet  MATH  Google Scholar 

  200. J. P. Jans, A note on injectives. Math. Ann., 175(3):239–242 (1968).

    MathSciNet  MATH  Google Scholar 

  201. C. U. Jensen, On characterizations of Prüfer rings. Math. Scand., 13(1):90–98 (1963).

    MathSciNet  MATH  Google Scholar 

  202. C. U. Jensen, A remark on flat and projective modules. Canad. J. Math., 18(5): 943–949 (1966).

    MathSciNet  MATH  Google Scholar 

  203. C. U. Jensen, A remark on semi-hereditary local rings. J.London Math. Soc., 41(3):479–482 (1966).

    MathSciNet  MATH  Google Scholar 

  204. C. U. Jensen, On homological dimensions of rings with countably generated ideals. Math. Scand., 18(2):97–105 (1966).

    MathSciNet  MATH  Google Scholar 

  205. C. U. Jensen, Homological dimensions of Ko-coherent rings. Math. scand., 20(1): 55–60 (1967).

    MathSciNet  MATH  Google Scholar 

  206. J.-P. Jouanlou, Sur la profondeur des modules de type fini. C. r. Acad. sci., 258(8):2245–2247 (1964).

    Google Scholar 

  207. T. Kanzaki, On commutator rings and Galois theory of separable algebras. Osaka J. Math., 1(1):103–115 (1964).

    MathSciNet  MATH  Google Scholar 

  208. I. Kaplansky, The homological dimension of a quotient field. Nagoya math. J., 27(1):139–142 (1966).

    MathSciNet  MATH  Google Scholar 

  209. K. Karták, On endomorphisms of the direct sum of two modules. Casop. pêstov. mat., 93(1):117–120 (1968).

    MATH  Google Scholar 

  210. F. Kaschand E. A. Mares, Eine Kennzeichnung semi-perfecter Moduln. Nagoya Math. J., 27(2):525–529 (1966).

    MathSciNet  Google Scholar 

  211. T. Kato, Duality of cyclic modules. Tôhoku Math. J., 19(3):349–356 (1967).

    MATH  Google Scholar 

  212. T. Kato, Self-injective rings. Tôhoku Math. J., 19(4):485–495 (1967).

    MATH  Google Scholar 

  213. T. Kato, Some generalizations of QF-rings. Proc. Japan Acad., 44(3):114–119 (1968).

    MathSciNet  MATH  Google Scholar 

  214. T, Kato, Torsionless modules. Tôhoku Math. J., 20(2):234–243 (1968).

    MATH  Google Scholar 

  215. S. M. Kaye, Ring theoretic properties of matrix rings. Canad. math. Bull., 10(3): 365–374 (1967).

    MathSciNet  MATH  Google Scholar 

  216. R. Kielpiñski, On -pure injective modules. Bull. Acad. polon. sci. Sér sci. math. astron. et phys., 15(3):127–131 (1967).

    MATH  Google Scholar 

  217. K. Kishimoto, On zeros of polynomials and Galois extensions of simple rings. J. Fac. Sci. Shinshu Unov., 2(2):117–122 (1967).

    MathSciNet  MATH  Google Scholar 

  218. K. Kishimoto, T. Onodera, and H. Tominaga, On the normal basis theorems and the extension dimension. J. Fac. Sci. Hokkaido Univ., Ser. 1, 18(1–2):8188 (1964).

    MathSciNet  Google Scholar 

  219. T. Klein, The multiplication of Schur-functions and extensions of p-modules. J. London Math. Soc., 43(2):280–284 (1968).

    MathSciNet  MATH  Google Scholar 

  220. I. Kleiner, Free and injective Lie modules. Canad. Math. Bull., 9(1):29–42 (1966).

    MathSciNet  MATH  Google Scholar 

  221. M. Knebusch, Flementarteilertheorie über Maximalordnungen. J. reine und angew. Math., 226:175–183 (1967).

    MathSciNet  MATH  Google Scholar 

  222. K. Koh, On simple rings with maximal annihilator right ideals. Canad. Math. Bull., 8(5):667–668 (1965).

    MathSciNet  MATH  Google Scholar 

  223. K. Koh, On some characteristic properties of self-injective rings. Proc. Amer. Math. Soc., 19(1):209–213 (1968).

    MathSciNet  MATH  Google Scholar 

  224. K. Koh, On a semiprimary ring. Proc. Amer. Math. Soc., 19 (1):205–208 (1968).

    MATH  Google Scholar 

  225. E. Kreindler, Remarques sur le théorème des facteurs invariants. Bull. Math. Soc. sci. mat. RSR, 11(2):181–186 (1967).

    MathSciNet  Google Scholar 

  226. E. Kreindler, Opérateurs pseudo-linéaires dans les modules unitaires. Rev. roumaine math. pures et appl., 13(2):201–234 (1968).

    MathSciNet  MATH  Google Scholar 

  227. R. S. Kulkarni, On a theorem of Jensen. Amer. Math. Monthly, 74(8):960–961 (1967).

    MathSciNet  MATH  Google Scholar 

  228. J.-P. Lafon, Spectre primier bilatère de l’anneau des endomorphismes d’un module de type fini. C. r. Acad. sci., 262(20):A1098–A1099 (1966).

    MathSciNet  Google Scholar 

  229. J.-P. Lafon, Spectre premier bilatère de l’anneau des endomorphismes d’un module de type fini. Bull Soc. Math. France, 94(4):269–275 (1967).

    MathSciNet  Google Scholar 

  230. J.-P. Lafon, Représentation d’algèbres comme quotients d’anneaux d’endomorphismes. Bull sci. math., 91(1–2):13–16 (1967).

    MathSciNet  MATH  Google Scholar 

  231. T.-Y. Lam, The category of Noetherian modules. Proc. Nat. Acad. Sci. USA, 55(5):1038–1040 (1966).

    MATH  Google Scholar 

  232. J. Lambek, Lectures on rings and modules, Blaisdell, Waltham (Mass.), (1966), 183 pp.

    MATH  Google Scholar 

  233. M. L. Laplaza, “Sobre la ordenacion de modulos,” Actas 5 reun. anual mat. esp. Valencia, 1964; Madrid (1967), pp. 221–224.

    Google Scholar 

  234. M. D. Larsen, Equivalent conditions for a ring to be aP-ring and a note on flat overrings. Duke Math. J., 34(2):273–280 (1967).

    MathSciNet  MATH  Google Scholar 

  235. D. Lazard, Algèbre symètrique et platitude. C. r. Acad. sci., 264(5):A228–A230 (1967).

    MathSciNet  Google Scholar 

  236. D. Lazard, Epimorphismes plats d’anneaux. C. r. Acad. sci., 266(6):A314–A316 (1968).

    MathSciNet  Google Scholar 

  237. W. G. Leavitt, The module type of homomorphic images. Duke Math. J., 32(2): 305–311 (1965).

    MathSciNet  MATH  Google Scholar 

  238. W. G. Leavitt, Type radicals. Glasgow Math. J., 9 (1):22–29 (1968).

    MathSciNet  MATH  Google Scholar 

  239. D. Legrand, Formes quadratiques et algèbres quadratiques. C. r. Acad. Sci., 265(23):A764–A767 (1967).

    MathSciNet  Google Scholar 

  240. C. Lemaire, Sur le complété d’un anneau-module topologique. Bull. cl. sci. Acad. roy. Belg., 52(3):390–394 (1966).

    MathSciNet  MATH  Google Scholar 

  241. W. W. Leonard, Small modules. Proc. Amer. Math. Soc., 17(2):527–531 (1966).

    MathSciNet  MATH  Google Scholar 

  242. L. S. Levy, Commutative rings whose homomorphic images are selfinjective. Pacif. J. Math., 18(1):149–153 (1966).

    MATH  Google Scholar 

  243. L. S. Levy, Decomposing pairs of modules. Trans. Amer. Math. Soc., 122(1):64–80 (1966).

    MathSciNet  MATH  Google Scholar 

  244. S. Lichtenbaum, On the vanishing of Tor in regular local rings. III. J. Math., 10(2):220–226 (1966).

    MathSciNet  MATH  Google Scholar 

  245. D. Lissner, Outer product rings. Trans. Amer. Math. Soc., 116(4):526–535 (1965).

    MathSciNet  MATH  Google Scholar 

  246. D. Lissner, OP-rings and Seshadri’s theorem. J. Algebra, 5(3):362–366 (1967).

    MathSciNet  MATH  Google Scholar 

  247. H. Lugowski, Die Charakterisierung gewisser geordneter Halbmoduln mit Hilfe der Erweiterungstheorie. Publs. math., 13(1–4):237–248 (1966).

    MathSciNet  MATH  Google Scholar 

  248. J. C. McConnel, Localisation in enveloping rings. J. London Math. Soc., 43(3): 421–428 (1968).

    MathSciNet  Google Scholar 

  249. I. G. Macdonald, Duality over complete local rings. Topology, 1:213–235 (July, 1962).

    MathSciNet  MATH  Google Scholar 

  250. S. MacLane, Homology, Springer, Berlin (1963), 422 pp.

    MATH  Google Scholar 

  251. B. H. Maddox, “Absolutely pure modules,” Doctoral dissertation, Univ. of South Carolina (1965), 31 pp.; Dissert. Abstr., 25(11):6658–6659 (1965).

    MathSciNet  Google Scholar 

  252. B. H. Maddox, Absolutely pure modules. Proc. Amer. Math. Soc., 18(1):155–158 (1967).

    MathSciNet  MATH  Google Scholar 

  253. M.-P. Malliavin, Modules sur les anneaux locaux réguliers. C. r. Acad. sci., 262(13):A736–A739 (1966).

    MathSciNet  Google Scholar 

  254. M.-P. Malliavin, Modules sur les anneaux locaux réguliers non ramifiés. C. r. Acad. sci., 262(14):A811–A812 (1966).

    MathSciNet  Google Scholar 

  255. M.-P. Malliavin-Brameret, Modules sur les anneaux locaux réguliers. Bull. Soc. math. France, 94(4):261–268 (1966).

    MathSciNet  MATH  Google Scholar 

  256. M.-P. Malliavin-Brameret, Largeurs d’anneaux et de modules. Bull Soc. math. France, 1966, 94(8):3–76 (1967).

    MathSciNet  Google Scholar 

  257. M.-P. Malliavin-Brameret, Modules de longueur finie sur un anneau régulier. C. r. Acad. sci., 264(3):A91–A94 (1967).

    MathSciNet  Google Scholar 

  258. M.-P. Malliavin-Brameret, Sous-anneaux non ramifiés d’anneaux réguliers. C. r. Acad. Sci., 264(9):A385–A387 (1967).

    MathSciNet  Google Scholar 

  259. J.-M. Maranda, Completions of modules and rings. Trans. Roy. Soc Canada, Sec 1–3, Vol. 3, pp. 271–291 (1965).

    MathSciNet  Google Scholar 

  260. H. Mascart, Sur Tutilisation de la polarité dans la théorie des modules topologiques. C. r. Acad. sci., 262(1):A16–A19 (1966).

    MathSciNet  Google Scholar 

  261. E. Matlis, Modules with descending chain condition. Trans. Amer. Math. Soc., 97:495–508 (1960).

    MathSciNet  Google Scholar 

  262. E. Matlis, Cotorsion modules. Mem. Amer. Math. Soc., No. 49 (1964), 66 pp.

    MathSciNet  Google Scholar 

  263. E. Matlis, Decomposable modules. Trans. Amer. Math. Soc., 125 (1):147–179 (1966).; correction, ibid., 134:315–324 (1968).

    MathSciNet  MATH  Google Scholar 

  264. E. Matlis, Reflexive domains. J. Algebra, 8 (1):1–33 (1968).

    MathSciNet  MATH  Google Scholar 

  265. C. K. Megibben, Modules over an incomplete discrete valuation ring. Proc. Amer. Math. Soc 19:450–452 (1968).

    MathSciNet  MATH  Google Scholar 

  266. G. Michler, Charakterisierung einer Klasse von Noetherschen Ringen. Math. Z., 100(2):163–182 (1967).

    MathSciNet  MATH  Google Scholar 

  267. B. Mitchell, Theory of Categories, Academic Press, New York (1965), 273 pp.

    MATH  Google Scholar 

  268. B. Mitchell, On the dimension of objects and categories. I. Monoids. J. Algebra, 9(3):314–340 (1968).

    MATH  Google Scholar 

  269. B. Mitchell, On the dimension of objects and categories. II. Finite ordered sets. J. Algebras, 9:341–368 (1968).

    MATH  Google Scholar 

  270. Y. Miyashita, Quasi-projective modules, perfect modules and a theorem for modular lattices. J. Fac. Sci. Hokkaido Univ., Ser. 1, 19(2):86–100 (1966).

    MathSciNet  MATH  Google Scholar 

  271. T. Miyata, Note on direct summands of modules. J. Math. Kyoto Univ., 7;65–69 (1967).

    MathSciNet  MATH  Google Scholar 

  272. H. Y. Mochizuki, On the double commutator algebra of QF-3 algebras. Nagoya Math. J., 25:221–230 (March, 1965).

    MathSciNet  MATH  Google Scholar 

  273. K. Morita, Duality for modules and its applications to the theory of rings with minimum condition. Sci.Repts. Tokyo Kyoiku Daigaku, A6:83–142 (May 15,1958).

    Google Scholar 

  274. K. Morita, Adjoint pairs functors and Frobenius extensions. Sci. Repts. Tokyo Kyoiku Daigaku, A9(202–208):40–71 (1965).

    Google Scholar 

  275. K. Morita, On S-rings in the sense of F. Kasch. Nagoya Math. J., 27(2):687–695 (1966).

    MathSciNet  MATH  Google Scholar 

  276. K. Morita, The endomorphism ring theorem for Frobenius extensions. Math. Z., 102(5):385–404 (1967).

    MathSciNet  MATH  Google Scholar 

  277. K. R. Mount, On polynomial rings. Mich. Math. J., 13(2):161–163 (1966).

    MathSciNet  MATH  Google Scholar 

  278. B. Muller, Quasi-Frobenius Erweiterungen. I. Math. Z., 85(4):345–368 (1964).

    MathSciNet  Google Scholar 

  279. B. Muller, Quasi-Frobenius Erweiterungen. II. Math. Z., 88(5):380–409 (1965).

    MathSciNet  Google Scholar 

  280. B. Muller, Über vollständige (Ko-) Homologie. Math. Ann., 165(3):223–235 (1966).

    MathSciNet  Google Scholar 

  281. B. Muller, On algebras of dominant dimension one. Nagoya Math. J., 31:173–183 (1968).

    MathSciNet  Google Scholar 

  282. B. Müller, The classification of algebras by dominant dimension. Canad. J. Math., 20(2):398–409 (1968).

    MathSciNet  MATH  Google Scholar 

  283. I. Murase, On the derivations of a quasi-matrix algebra. Scient. Papers Coll. Gen. Educ. Univ. Tokyo, 14(2):157–164 (1964).

    MathSciNet  MATH  Google Scholar 

  284. M. P. Murthy, Projective modules over a class of polynomial rings. Math. Z., 88(2):184–189 (1965).

    MathSciNet  MATH  Google Scholar 

  285. M. P. Murthy, Projective A(X)-modules. J. London Math. Soc., 41(3):453–456 (1966).

    MathSciNet  MATH  Google Scholar 

  286. M. Narita, Weak topologies and injective modules. Proc. Japan. Acad., 43(1): 6–10 (1967).

    MathSciNet  MATH  Google Scholar 

  287. C. Nstsescu, Sur une classe d’anneaux. C. r. Acad. sci., 266(19):A966–A969 (1968).

    Google Scholar 

  288. C. Nstsescu and N. Popescu, Sur la structure des objets de certaines categories abéliennes. C. r. Acad. sci., AB262(24):A1295–A1297 (1966).

    Google Scholar 

  289. C. Nstsescu and N. Popescu, Quelques observations sur les topos abéliens. Rev. roumaine math. pures et appl., 12(4):551–563 (1967).

    Google Scholar 

  290. N. Nobusawa, On lattices in a module over a matrix algebra. Canad. Math. Bull., 9 (1):57–6l (1966).

    MathSciNet  MATH  Google Scholar 

  291. N. Nobusawa, Structure theorems of a module over a ring with a bilinear mapping. Canad. Math. Bull., 10(5):649–652 (1967).

    MathSciNet  MATH  Google Scholar 

  292. D. G. Northcott and M. Reufel, Contributions to the specialization theory of polynomial modules. Proc. Roy Soc., A281(1386):291–309 (1964).

    MathSciNet  Google Scholar 

  293. D. G. Northcott and M. Reufel, A generalization of the concept of length. Quart. J. Math., 16(64):297–32l (1965).

    MathSciNet  MATH  Google Scholar 

  294. A. P. Northover, Modules over a one-dimensional local ring. Quart. J. Math., 17(67):195–210 (1966).

    MathSciNet  MATH  Google Scholar 

  295. J.-P. Oliver, Anneauxabsolument plats universles et épimorphismes d’anneaux. C. r. Acad. sci., 266(6):A317–A318 (1968).

    Google Scholar 

  296. T. Onodera, Some studies on projective Frobenius extensions. J. Fac. Sci. Hokkaido Univ., Ser. 1, 18(1–2)189–107 (1967).

    Google Scholar 

  297. B. L. Osofsky, A counter example to a lemma of Skornjakov. Pacif. J. Math., 15(3):985–987 (1965).

    MathSciNet  MATH  Google Scholar 

  298. B. L. Osofsky, Cyclic injective modules of full linear rings. Proc. Amer. Math. Soc., 17(1):247–253 (1966).

    MathSciNet  MATH  Google Scholar 

  299. B. L. Osofsky, A generalization of quasi-Frobenius rings. J. Algebra, 4:373–387 (1966): correction, ibid.. 8:41–44 (1968).

    MathSciNet  MATH  Google Scholar 

  300. B. L. Osofsky, Global dimension of valuation rings. Trans. Amer. Math. Soc., 127(1):136–149 (1967).

    MathSciNet  MATH  Google Scholar 

  301. B. L. Osofsky, A non-trivial ring with non-rational injective hull. Canad. Math. Bull., 10(2):275–282 (1967).

    MathSciNet  MATH  Google Scholar 

  302. B. L. Osofsky, Upper bounds on homological dimensions. Nogoya Math. J., 32: 315–322 June, (1968).

    MathSciNet  MATH  Google Scholar 

  303. B. L. Osofsky, Endomorphisms rings of quasi-injective modules. Canad. J. Math., 20(4):895–903 (1968).

    MathSciNet  MATH  Google Scholar 

  304. B. L. Osofsky, Noncommutative rings whose cyclic modules have cyclic injective hulls. Pacif. J. Math., 25:331–340 (1968).

    MathSciNet  MATH  Google Scholar 

  305. B. L. Osofsky, Homological dimension and the continuum hypothesis. Trans. Amer. Math. Soc., 132:217–230 (1968).

    MathSciNet  MATH  Google Scholar 

  306. B. Pareigis, Einige Bemerkungen über Frobenius Erweiterungen. Math. Ann., 153(1):1–13 (1964).

    MathSciNet  Google Scholar 

  307. B. Pareigis, “Radikale und kleine Moduln,” Sitzungsber. Bayer. Akad. Wiss. München, Math.-naturwiss. Kl. (1965), München (1966), pp. 185–199.

    Google Scholar 

  308. B. Pareigis, Vergessende Funktoren und Ringhomomorphismen. Math. Z., 93(4): 265–275 (1966).

    MathSciNet  MATH  Google Scholar 

  309. E. M. Patterson, The Jacobson radical of a pseudo-ring. Math. Z., 89(4):348–364 (1965).

    MathSciNet  MATH  Google Scholar 

  310. R. E. Peinado, Una clasificación de anillos. Rev. mat. hisp.-amer., 25(6):249–261 (1965).

    MathSciNet  MATH  Google Scholar 

  311. R. E. Peinado and W. G. Leawitt, The maxit and minit of a ring. Proc. Glasgow Math. Assoc, 7:128–135 (1966).

    MathSciNet  MATH  Google Scholar 

  312. J. C. Pleasant, “Certain relations between objects and morphisms in arbitrary categories and module categories,” Doctoral dissertation, Univ. of South Carolina (1965), 51 pp.; Dissert. Abstr., 26(8):4697 (1966).

    Google Scholar 

  313. N. Popescu and A. Radu, La structure des modules injectifs sur un anneau à ideal principal. Bull. Math. Soc. sci. math. etphys.RPR, 8(1–2):67–73 (1964).

    MathSciNet  Google Scholar 

  314. Y. Quentel, Sur une caractérisation des anneaux de valuation de hauteur. C. r. Acad. Sci., 265(21):A659–A661 (1967).

    MathSciNet  Google Scholar 

  315. Y. Quentel, Sur une caractrisation des anneaux semihérédiaires. commutatifs. C. r. Acad. Sci., No. 5, pp. A266–A267 (1968).

    MathSciNet  Google Scholar 

  316. A. Radu, Functia caracteristic a lui Hilbert. Studii i cercetri mat. Acad. RSR, 19(4):537–547 (1967).

    MathSciNet  MATH  Google Scholar 

  317. N. Radu, Asupra functorului de completare, Studii i cercetri mat. Acad. RSR, 17(7):1077–1087 (1965).

    MathSciNet  MATH  Google Scholar 

  318. N. Radu, Sur les anneaux coherénts laskériens. Rev. roumaine de math. pures et appl., Acad. RSR, 11(7):865–867 (1966).

    MathSciNet  MATH  Google Scholar 

  319. N. Radu, Module de S-cotorsiune. An. Univ. Bucuresti. Ser. tiin. natur. Mat. mecan., 15(2):25–32 (1966).

    MathSciNet  MATH  Google Scholar 

  320. N. Radu, Sur la décomposition primaire des modules. Bull math. Soc. sci. math. RSR, 10(1–2):143–149 (1966).

    MathSciNet  Google Scholar 

  321. N. Radu, Asupra unor categorii de module. Studii i cercetri mat. Acad. RSR, 19(3):393–402 (1967).

    MathSciNet  MATH  Google Scholar 

  322. C. F. F. Raggi, Localizaction en anillos no commutativos. An. Inst. mat. Univ. nac. autónoma Mexico, 6:1–6 (1966).

    MATH  Google Scholar 

  323. L. J. Ratliff, On finite modules over a Noetherian domain. III. J. Math., 10(1): 56–60 (1966).

    MathSciNet  MATH  Google Scholar 

  324. J. Ravel, Objects spéciaux dans certaines catégories. C. r. Acad. sci., 264(5): 226–227 (1967).

    MathSciNet  MATH  Google Scholar 

  325. J. Ravel, Extensions essentielles dans un module, C. r. Acad. sci., 264(15): A657–A659 (1967).

    MathSciNet  Google Scholar 

  326. M. Raynaud, Solution d’un problème universel relatif aux modules projectifs de type fini. C. r. Acad. sci., 260(17):4391–4394 (1965).

    MathSciNet  MATH  Google Scholar 

  327. I. Reiner, Module extensions and blocks. J. Algebra, 5(2):I57-I63 (1967).

    MathSciNet  MATH  Google Scholar 

  328. G. Renault, Etude des sous-modules compléments dans un A-module. Sémin. Dubreil et Pisot. Fac. Sci. Paris, 16(2):16/01–16/12 (1967).

    Google Scholar 

  329. G. Renault, Anneaux self-injectifs. Sémin. Dubreil et Pisot. Fac. Sci. Paris, l9 (1):11/01–11/04 (1967).

    Google Scholar 

  330. G. Renault, Etude des anneaux réduits et de leurs enveloppes injectives. C. r. Acad. sci., 264(2):A53–A55 (1967).

    MathSciNet  Google Scholar 

  331. G. Renault, Sur les anneaux A tels que tout A-module a gauche non nul contient un soud-module maximal. C. r. Acad. sci., 264(14):A622–A624 (1967).

    MathSciNet  Google Scholar 

  332. G. Renault, Anneaux assocíé à un module injectif. C. r. Acad. sci., 264(26): A1163–A1164 (1967).

    MathSciNet  Google Scholar 

  333. G. Renault, “Etude des sous-modules complements dans un module,” Bull. Soc. Math. France, Vol. 95, Mem. No. 9, 79 pp. (1967).

    MathSciNet  Google Scholar 

  334. G. Renault, Anneaux réduits non commutatifs. J. Math. pures et appl., 46(2): 203–214 (1967).

    MathSciNet  MATH  Google Scholar 

  335. G. Renault, Anneau associé a un module injectif. Bull. sci. math., 92(1–2):53–58 (1968).

    MathSciNet  MATH  Google Scholar 

  336. R. Rentschier, Eine Bemerkung zu Ringen mit Minimalbedingung für Hauptideale. Arch. Math., 17(4):298–301 (1966).

    Google Scholar 

  337. R. Rentschier and P. Gabriel, Sur la dimension des anneaux et ensembles ordonnés. C. r. Acad. sci., 265(22):A7I2–A7I5 (1967).

    Google Scholar 

  338. M. Reufei, Konstruktionsverfahren bei Modulnüber Polynomringen. Math. Z., 90(3):231–250 (1965).

    MathSciNet  Google Scholar 

  339. P. Ribenboim, On the completion of a valuation ring. Math. Ann., 155(5):392–396 (1964).

    MathSciNet  MATH  Google Scholar 

  340. P. Ribenboim, On ordered modules. J. reine und angew. Math., 225:120–146 (1967): correction, ibid., 238:132–134 (1969).

    MathSciNet  MATH  Google Scholar 

  341. F. Richman, Generalized quotient rings. Proc. Amer. Math. Soc., 16(4):794–799 (1965).

    MathSciNet  MATH  Google Scholar 

  342. F. Richman and E. A. Walker, Cotorsion free, an example of relative injectivity. Math. Z., 102(2):115–117 (1967).

    MathSciNet  MATH  Google Scholar 

  343. M. A. Rieffel, A general Wedderburn theorem. Proc. Nat. Acad. Sci. USA, 54(6): 1513 (1965).

    MathSciNet  Google Scholar 

  344. “Ringe und Moduln,” Tagungsbericht 27 Feb.-5 März, 1966, Math. Forschungsinst., Oberwolfach (1966), 14 pp.

    Google Scholar 

  345. J.-E. Roos, Caractérisation des catégories qui sont quotients de catégories de modules par des sous-catégories bilocalisants. C. r. Acad. sci., 261(23):4954–4957 (1965).

    MathSciNet  MATH  Google Scholar 

  346. A. Roy, A note on filtered rings. Arch. Math., 16(6):421–427 (1965).

    MathSciNet  MATH  Google Scholar 

  347. E. A. Rutter, Jr., A remark concerning quasi-Frobenius rings. Proc. Amer. Math. Soc., 16(6):1372–1373 (1965).

    MathSciNet  MATH  Google Scholar 

  348. P. Samuel, Anneaux gradués factoriels et modules réflexifs. Bull. Soc. math. France, 92(2):237–249 (1964).

    MathSciNet  MATH  Google Scholar 

  349. P. Samuel, Modules réflexifs et anneaux factoriels. Colloq. internat. Centre nat. rech. scient., 143:219–223 (1966).

    MathSciNet  MATH  Google Scholar 

  350. P. Samuel, “Modules réflexifs et anneaux factoriels,” in; Les Tendances Géométriques en Algèbre et Théorie des Nombres (1966), pp. 219–223.

    Google Scholar 

  351. P. Samuel, Modules réflexifs et anneaux factoriels. Sémin.Dubreilet Pisot. Fac. Sci., Paris, 17 (1):8/01–8/04 (1967).

    MathSciNet  Google Scholar 

  352. D. F. Sanderson, A generalization of divisibility and injectivity in modules. Canad. Math. Bull., 8(4):505–513 (1965).

    MathSciNet  MATH  Google Scholar 

  353. F. L. Sandomierski, “Relative injectivity and projectivity,” Doctoral dissertation Pennsylvania State Univ. (1964) 67 pp.; Dissert. Abstr., 25(11):6664 (1965).

    Google Scholar 

  354. F. L. Sandomierski, Nonsingular rings. Proc. Amer. Math. Soc., 19(1):225–230 (1968).

    MathSciNet  MATH  Google Scholar 

  355. D. A. Sankowsky, “Relative homo logical dimensions of rings and modules,” Doctoral dissertation, Univ. California, Berkeley (1967), 44 pp. Dissert. Abstr., B28(10):4206 (1968).

    Google Scholar 

  356. M. Satyanarayana, Rings with primary ideals as maximal ideals. Math. Scand., 20 (1):52–54 (1967).

    MathSciNet  MATH  Google Scholar 

  357. M. Satyanarayana, Semisimple rings. Amer. Math. Monthly, 74(19):1086 (1967).

    MathSciNet  MATH  Google Scholar 

  358. M. Satyanarayana, Characterization of local rings. Tohoku Math. J., 19(4):411–416 (1967).

    MathSciNet  MATH  Google Scholar 

  359. J.-P. Serre, Sur les modules projectifs, Sémin P. Dubreil, M-L Dubreil-Jacotin et C. Pisot; Fac. sci. Paris, 1960–1961, 14 année, fasc. 1, Paris 2/01–2/16 (1963).

    Google Scholar 

  360. C. S. Seshadri, Triviality of vector bundles over the affine space K2. Proc. Nat. Acad. Sci. USA, 44(5):456–458 (1958).

    MathSciNet  MATH  Google Scholar 

  361. C. S. Seshadri, Algebraic vector bundles over the product of an affine curve and the line. Proc. Amer. Math. Soc., 10(5):670–673 (1959).

    MathSciNet  MATH  Google Scholar 

  362. L. Silver, Noncommutative localizations and applications. J. Algebra, 7 (1):44–76 (1967).

    MathSciNet  MATH  Google Scholar 

  363. L. W. Small, An example in Noetherian rings. Proc. Nat. Acad. Sci. USA, 54(4): 1035–1036 (1965).

    MathSciNet  MATH  Google Scholar 

  364. L. W. Small, “Some remarks on the homological dimensions of a quotient field,” Mimeographed notes, Univ. of California, Berkeley, Calif. (1966).

    Google Scholar 

  365. L. W. Small, Hereditary rings. Proc. Nat. Acad. Sci. USA, 55:25–27 (1966).

    MathSciNet  MATH  Google Scholar 

  366. L. W. Small, On some questions in Noetherian rings. Bull. Amer. Math. Soc., 72(5):853–857 (1966).

    MathSciNet  MATH  Google Scholar 

  367. L. W. Small, Orders in Artinian rings. J. Algebra, 4(1):13–41 (1966).

    MathSciNet  MATH  Google Scholar 

  368. L. W. Small, Semihereditary rings. Bull. Amer. Math. Soc., 73(5):656–658 (1967).

    MathSciNet  MATH  Google Scholar 

  369. L. W. Small, Correction and addendum: Orders in Artinian rings. J. Algebra, 4:505–507 (1966).

    MathSciNet  Google Scholar 

  370. L. W. Small, Orders in Artinian rings. II. J. Algebra, 9(3):266–273 (1968).

    MathSciNet  MATH  Google Scholar 

  371. L. W. Small, A change of rings theorem. Proc. Amer. Math. Soc., 19(3):662–666 (1968).

    MathSciNet  MATH  Google Scholar 

  372. D. A. Smith, Chevalley bases for Lie modules. Trans. Amer. Math. Soc., 115(3): 283–299 (1965).

    MathSciNet  MATH  Google Scholar 

  373. E. Snapper, Injective modules under change of rings. Proc. Amer. Math. Soc., 16(4):788–790 (1965).

    MathSciNet  MATH  Google Scholar 

  374. A. Solian, Characterization of some functors of modules. Rev. roumaine math. pures et appl 11(3):283–285 (1966).

    MathSciNet  MATH  Google Scholar 

  375. A. Solian, Foncteurs qui transforment les épimorphismes locaux en monomorphismes locaux. Rev. roumaine math. pures et appl., 11(4):401–410 (1966).

    MathSciNet  MATH  Google Scholar 

  376. R. Sridharan, Homo logy of non-commutative polynomial rings. Nagoya Math. J., 26 (1):53–59 (1966).

    MathSciNet  MATH  Google Scholar 

  377. O. tnail, Citeva observaii asupra topologizrii modulelor. Studii i cercetlri mat. Acad. RSR, 18(5):681–686 (1966).

    Google Scholar 

  378. A. Steger, Diagonability of idempotent matrices. Pacif. J. Math., l9(3):535–542 (1966).

    MathSciNet  MATH  Google Scholar 

  379. B. T. Stenström, Pure submodules. Arkiv mat., 7(2):159–171 (1967).

    MATH  Google Scholar 

  380. B. T. Stenström, High submodules and purity. Arkiv mat., 7(2):173–176 (1967).

    MATH  Google Scholar 

  381. R. W. Stringall, Endomorphism rings of primary Abelian groups. Pacif. J. Math., 20(3):535–557 (1967).

    MathSciNet  MATH  Google Scholar 

  382. J. R. Strooker, Lifting projectives. Nagoya Math. J., 27(2):747–751 (1966).

    MathSciNet  MATH  Google Scholar 

  383. A. Sugano, A note on Azumaya’s theorem. Osaka J. Math., 4(1):I57-I6O (1967): correction ibid., 5:153 (1968).

    MathSciNet  MATH  Google Scholar 

  384. A. Sugano, Note on semisimple extensions and separable extensions. Osaka J. Math., 4(2):265–270 (1967).

    MathSciNet  MATH  Google Scholar 

  385. S. Suzuki, Note on formally projective modules. J. Math. Kyoto Univ., 5(3): 193–196 (1966).

    MathSciNet  MATH  Google Scholar 

  386. Y. Suzuki, On automorphisms of an injective module. Proc. Japan Acad., 44(3): 120–124 (1968).

    MathSciNet  MATH  Google Scholar 

  387. R. G. Swan, Induced representations and projective modules. Ann. Math., 71(3): 552–578 (1960).

    MathSciNet  MATH  Google Scholar 

  388. R. G. Swan, The number of generators of a module. Math. Z., 102(4):318–322 (1967).

    MathSciNet  MATH  Google Scholar 

  389. F. Szász, Einige Kriterien für die Existenz des Einselementes in einem Ring. Acta scient. math., 28(1–2):31–37 (1967).

    MATH  Google Scholar 

  390. H. Tachikawa, On dominant dimensions of QF-3 algebras. Trans. Amer. Math. Soc., 112(2):249–266 (1964).

    MathSciNet  MATH  Google Scholar 

  391. G. Thierrin, Anneaux métaprimitifs. Canad. J. Math., 17 (1):199–205 (1965).

    MathSciNet  MATH  Google Scholar 

  392. K. Tiwari, On complete ring of quotients. J. Indian Math. Soc., 31(2):95–99 (1967).

    MathSciNet  MATH  Google Scholar 

  393. A. K. Tiwary, On the quotients of indecomposable injective modules. Canad. Math. Bull., 9(2):187–190 (1966).

    MathSciNet  MATH  Google Scholar 

  394. Chi-te Tsai, Report on injective modules. Queen’s Papers Pure and Appl. Math., No. 6, 243 pp. (1966).

    Google Scholar 

  395. K. Uchida, A note on the projective modules over group rings. Proc. Japan Acad., 43(1):13–16 (1967).

    MathSciNet  MATH  Google Scholar 

  396. Y. Utumi, On continuous rings and self injective rings. Trans. Amer. Math. Soc., 118(6):158–173 (1965).

    MathSciNet  MATH  Google Scholar 

  397. Y. Utumi, On the continuity and self-injectivity of a complete regular ring. Canad. J. Math., 18(2):404–412 (1966).

    MathSciNet  MATH  Google Scholar 

  398. Y. Utumi, Self-injective rings. J. Algebra, 6 (1):56–64 (1967).

    MathSciNet  MATH  Google Scholar 

  399. P. Vámos, On ring classes defined by modules. Publs. math., 14(1–4):1–8 (1967).

    MATH  Google Scholar 

  400. P. Vámos, The dual of the notion of “finitely generated”. J. London Math. Soc., 43:643–646 (1968).

    MathSciNet  MATH  Google Scholar 

  401. B. J. Varela, Une note sur des modules élastiques. Rev. colomb. mat., 1(3):26–28 (1967).

    MATH  Google Scholar 

  402. W. V. Vasconcelos, On local and stable cancellation. An. Acad. brasil. ciênc, 37(3–4):389–393 (1965).

    MathSciNet  MATH  Google Scholar 

  403. W. V. Vasconcelos, R-sequences and the homology of Macaulay rings. An. Acad. brasil ciênc, 38(2):249–252 (1966).

    MathSciNet  MATH  Google Scholar 

  404. W. V. Vasconcelos, Ideals and cancellation. Math. Z., 102(5):353–355 (1967).

    MathSciNet  MATH  Google Scholar 

  405. O. E. Villamayor, Sur une representation matricielle de l’anneaux d’endomorphismes d’un module quelconque. Publs. Fac cienc fisicomat. Univ. nac La Plata, No. 213, pp. 185–190 (1956).

    MathSciNet  Google Scholar 

  406. C. P. Walker, Relative homological algebra and Abelian groups. III. J. Math., 10(2):186–209 (1966).

    MATH  Google Scholar 

  407. C. L. Walker and E. A. Walker “Quotient categories of modules,” Proc. conf. categor. algebra (1966), pp. 404–420.

    Google Scholar 

  408. Y. Watanabe, Simple algebras over a complete local ring. Osaka J. Math., 3 (1):13–20 (1966).

    MathSciNet  MATH  Google Scholar 

  409. R. H. Wenger, “Semigroups having qasi-Frobenius algebras,” Doctoral dissertation, Michigan State Univ. (1965), 70 pp.; Dissert. Abstr., 26(8):4703 (1966).

    Google Scholar 

  410. E. R. Willard, “Functors between categories of modules,” Doctoral dissertation, Pennsylvania State Univ. (1964), 81 pp,Dissert. Abstr. 25(11):6668–6669 (1965).

    Google Scholar 

  411. E. R. Willard, Properties of projective generators. Math. Ann., 158(5):352–364 (1965).

    MathSciNet  MATH  Google Scholar 

  412. Ling-Erl Eileen Ting Wu, A characterization of self-injective rings. Ill. J. Math., 10 (1):61–65 (1966).

    Google Scholar 

  413. Ling-Erl Eileen Ting Wu and J. P. Jans, On quasi projectives. Ill. J. Math., 11(3): 439–448 (1967).

    Google Scholar 

  414. Ling-Erl Eileen Ting Wu, H. Y. Mochizuki, and J. P. Jans, A characterization of QF-3 rings. Nagoya Math. J., 27(1):7–13 (1967).

    Google Scholar 

  415. F. Wuytack and J. Depunt, Operators over I-collections of modules. Bull. Soc. math. Belg., 17 (1):37–54 (1965).

    MathSciNet  MATH  Google Scholar 

  416. F. Wuytack and J. Depunt, Note on I-collections of modules. Bull Soc. math. Belg., 17(4):484–494 (1965).

    MathSciNet  MATH  Google Scholar 

  417. C. R. Yohe, Triangular and diagonal forms for matrices over commutative noe-therian rings. J. Algebra, 6(3):335–368 (1967).

    MathSciNet  MATH  Google Scholar 

  418. A. Zaka, Residue rings of semi-primary hereditary rings. Nagoya Math. J., 30:279–283 (Aug. 1967).

    MathSciNet  Google Scholar 

  419. A. Zaks, Global dimension of Artinian rings. Proc. Amer. Math. Soc., 18(6): 1102–1106 (1967).

    MathSciNet  MATH  Google Scholar 

  420. A. Zaka, A note on semi-primary hereditary rings. Pacif. J. Math., 23:627–628 (1967).

    Google Scholar 

  421. H. Zassenhaus, Orders as endomorphism rings of modules of the same rank. J. London Math. Soc., 42:180–182 (1967).

    MathSciNet  MATH  Google Scholar 

  422. J. M. Zelmanowitz, Endomorphism rings of torsionless modules. 5(3):325–341 (1967).

    MathSciNet  MATH  Google Scholar 

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  1. A. V. Mikhalev
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  1. V. A. Steklov Mathematics Institute, Academy of Sciences of the USSR, Moscow, Russia

    R. V. Gamkrelidze

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Mikhalev, A.V., Skornyakov, L.A. (1972). Modules. In: Gamkrelidze, R.V. (eds) Algebra and Geometry. Progress in Mathematics, vol 12. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-0507-2_2

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