Homological properties of coherent semilocal rings

Cheng, Fu Chang; Zhao, Yi Cai; Tang, Gao Hua

doi:10.1090/S0002-9939-1990-1028043-1

Homological properties of coherent semilocal rings
HTML articles powered by AMS MathViewer

by Fu Chang Cheng, Yi Cai Zhao and Gao Hua Tang

Proc. Amer. Math. Soc. 110 (1990), 39-44

DOI: https://doi.org/10.1090/S0002-9939-1990-1028043-1

PDF | Request permission

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

M. F. Atiyah and I. G. Macdonald, Introduction to commutative algebra, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1969. MR 0242802

On the structure of coherent

rings

Jim Zhong Xu, The modules over a semilocal ring and their homological dimension, Chinese Ann. Math. Ser. A 7 (1986), no. 6, 685–691 (Chinese). An English summary appears in Chinese Ann. Math. Ser. B 8 (1987), no. 1, 129. MR 886740
Irving Kaplansky, Commutative rings, Revised edition, University of Chicago Press, Chicago, Ill.-London, 1974. MR 0345945
Irving Kaplansky, Fields and rings, University of Chicago Press, Chicago, Ill.-London, 1969. MR 0269449
Hideyuki Matsumura, Commutative algebra, 2nd ed., Mathematics Lecture Note Series, vol. 56, Benjamin/Cummings Publishing Co., Inc., Reading, Mass., 1980. MR 575344
Ho Kuen Ng, Coherent rings of dimension two, Proc. Amer. Math. Soc. 91 (1984), no. 4, 518–522. MR 746080, DOI 10.1090/S0002-9939-1984-0746080-6
Ho Kuen Ng, Finitely presented dimension of commutative rings and modules, Pacific J. Math. 113 (1984), no. 2, 417–431. MR 749546
D. G. Northcott, A first course of homological algebra, Cambridge University Press, London, 1973. MR 0323867
D. G. Northcott, An introduction to homological algebra, Cambridge University Press, New York, 1960. MR 0118752

Critères de platitude et de projectivité

13

Joseph J. Rotman, An introduction to homological algebra, Pure and Applied Mathematics, vol. 85, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1979. MR 538169
Wolmer V. Vasconcelos, The local rings of global dimension two, Proc. Amer. Math. Soc. 35 (1972), 381–386. MR 308115, DOI 10.1090/S0002-9939-1972-0308115-6
Wolmer V. Vasconcelos, The rings of dimension two, Lecture Notes in Pure and Applied Mathematics, Vol. 22, Marcel Dekker, Inc., New York-Basel, 1976. MR 0427290