Certain countably generated big Cohen-Macaulay modules are balanced

Author:

Sharp R. Y.

Abstract

Throughout this note, A will denote a (commutative, Noetherian) local ring (with identity) having maximal ideal m and dimension d. Let x1, …, xd be a system of parameters (s.o.p.) for A. A (not necessarily finitely generated) A-module M is said to be a big Cohen–Macaulay A-module with respect to x1, …, xd, if x1, …, xd is an M-sequence. In the last ten or fifteen years there has been substantial interest in such modules, initially stemming from M. Hochster's discoveries that, if A contains a field as a subring, and x1, …,xd is any s.o.p. for A, then there exists a big Cohen-Macaulay A-module with respect to x1, …,xd, and that the existence of such modules has important consequences for the local homological conjectures in commutative algebra: see [6].

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Cited by 3 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Finite Phantom Projective Dimension;American Journal of Mathematics;1994-04

2. A generalization of a theorem of Sharp on big Cohen-Macaulay modules;Mathematical Proceedings of the Cambridge Philosophical Society;1990-09

3. Infinite coverings of ideals by cosets with applications to regular sequences and balanced big Cohen–Macaulay modules;Mathematical Proceedings of the Cambridge Philosophical Society;1990-05

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