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Transactions of the American Mathematical Society

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Finitistic dimension and a homological generalization of semi-primary rings


Author: Hyman Bass
Journal: Trans. Amer. Math. Soc. 95 (1960), 466-488
MSC: Primary 16.90; Secondary 16.40
DOI: https://doi.org/10.1090/S0002-9947-1960-0157984-8
MathSciNet review: 0157984
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  • [1] M. Auslander, On the dimension of modules and algebras, III, Nagoya Math. J. vol. 9 (1955) pp. 67-77. MR 0074406 (17:579a)
  • [2] -, On regular group rings, Proc. Amer. Math. Soc. vol. 8 (1957) pp. 658-664. MR 0087670 (19:390a)
  • [3] M. Auslander and D. Buchsbaum, Homological dimension in local rings, Trans. Amer. Math. Soc. vol. 85 (1957) pp. 390-405. MR 0086822 (19:249d)
  • [4] H. Bass, Finitistic dimension in Noetherian rings, (in preparation.)
  • [5] H. Cartan and S. Eilenberg, Homological algebra, Princeton University Press, 1956. MR 0077480 (17:1040e)
  • [6] J. Dieudonné, Remarks on quasi-Frobenius rings, Illinois J. Math. vol. 2 (1958) pp. 346-354. MR 0097427 (20:3896)
  • [7] B. Eckmann and A. Schopf, Über injective moduln, Arch. Math. vol. 4 (1953) pp. 75-78. MR 0055978 (15:5d)
  • [8] S. Eilenberg, Homological dimension and syzygies, Ann. of Math. vol. 64 (1956) pp. 328-336. MR 0082489 (18:558c)
  • [9] S. Eilenberg and T. Nakayama, On the dimension of modules and algebras, V, Nagoya Math. J. vol. 11 (1957) pp. 9-12. MR 0086070 (19:118f)
  • [10] M. Harada, Note on the dimension of modules and algebras, J. Inst. Polytech. Osaka City Univ. Ser. A, vol. 7 (1956) pp. 17-27. MR 0081269 (18:375d)
  • [11] N. Jacobson, Structure of rings, Amer. Math. Soc. Colloquium Publications, vol. 37, 1956. MR 0081264 (18:373d)
  • [12] E. Matlis, Injective modules over Noetherian rings, Pacific J. Math. vol. 8 (1958) pp. 511-528. MR 0099360 (20:5800)
  • [13] K. Morita, Duality for modules and its applications to the theory of rings with minimum condition, Science Reports, Tokyo Kyoiku Daigaku, vol. 6, 1958, pp. 83-142. MR 0096700 (20:3183)
  • [14] J. P. Serre, Sur la dimension homologique des anneaux et des modules Noethériens, Proceedings International Symposium on Algebraic Number Theory, Tokyo and Nikko, 1955, pp. 175-189. MR 0086071 (19:119a)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1960-0157984-8
Article copyright: © Copyright 1960 American Mathematical Society

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