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Defective big Cohen-Macaulay modules

Published online by Cambridge University Press:  24 October 2008

M. L. Brown
M. L. Brown
Affiliation:
University College, Cardiff
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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

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References

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