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Defective big Cohen-Macaulay modules
Published online by Cambridge University Press: 24 October 2008
Extract
Let R be a noetherian local ring and x = x1, …, xn a system of parameters for R. If R is an equicharacteristic local ring then Hochster(3) proved there is a big Cohen-Macaulay module with respect to x, i.e. an R-module M, not necessarily noetherian, with x1, …, xn a regular sequence on M and M/(x) M ≠ 0. Such modules are important for the study of the homological conjectures in commutative algebra(3). Nevertheless, for mixed characteristic local rings virtually nothing is known about their existence.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 93 , Issue 2 , March 1983 , pp. 253 - 257
- Copyright
- Copyright © Cambridge Philosophical Society 1983
References
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