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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Homological properties of coherent semilocal rings


Authors: Fu Chang Cheng, Yi Cai Zhao and Gao Hua Tang
Journal: Proc. Amer. Math. Soc. 110 (1990), 39-44
MSC: Primary 13D05
MathSciNet review: 1028043
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Abstract: W. V. Vasconcelos and M. Auslander have studied the homological properties of coherent (noetherian) rings. In [3] some theorems for regular local rings were generalized to noetherian semilocal rings. The main aim of this paper is to discuss coherent semilocal rings.


References [Enhancements On Off] (What's this?)

  • [1] M. F. Atiyah and I. G. MacDonald, Introduction to commutative algebra, Addison-Wesley Reading, MA, 1969. MR 0242802 (39:4129)
  • [2] C. Fuchang and Z. Yicai, On the structure of coherent $ FP$-rings, Ann. Chinese Math. (to appear).
  • [3] X. Jinzhong, The modules over a semilocal ring and their homological dimension, Ann. Chinese Math. 6 (1986), 685-691. MR 886740 (88d:13025)
  • [4] I. Kaplansky, Commutative rings, Univ. of Chicago Press, Chicago, 1974. MR 0345945 (49:10674)
  • [5] -, Fields and rings, Univ. of Chicago Press, Chicago, 1969. MR 0269449 (42:4345)
  • [6] H. Matsumura, Commutative algebra (2nd ed.), Benjamin/Cummings, 1980. MR 575344 (82i:13003)
  • [7] H. K. Ng, Coherent rings of dimension two, Proc. Amer. Math. Soc. 91 (1984), 518-522. MR 746080 (85j:13023)
  • [8] -, Finitely presented dimension of commutative rings and modules, Pacific J. Math. 113 (1984), 417-431. MR 749546 (85h:13010)
  • [9] D. C. Northcott, A first course of homological algebra, Cambridge University Press, Cambridge, 1973. MR 0323867 (48:2220)
  • [10] -, An introduction to homological algebra, Cambridge University Press, Cambridge, 1960. MR 0118752 (22:9523)
  • [11] G. Raynaud, Critères de platitude et de projectivité, Invent. Math. 13 (1971).
  • [12] J. J. Rotman, An introduction to homological algebra, Academic Press, New York, 1979. MR 538169 (80k:18001)
  • [13] W. V. Vasconcelos, The local rings of global dimension two, Proc. Amer. Math. Soc. 35 (1972), 381-385. MR 0308115 (46:7230)
  • [14] -, The rings of dimension two, Marcel Dekker, 1976. MR 0427290 (55:324)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1990-1028043-1
PII: S 0002-9939(1990)1028043-1
Article copyright: © Copyright 1990 American Mathematical Society