Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4588510 | Journal of Algebra | 2007 | 12 Pages |
Abstract
A higher syzygy of a module with positive codimension is a maximal Cohen–Macaulay module that plays an important role in Cohen–Macaulay approximation over Gorenstein rings. We show that every maximal Cohen–Macaulay module is a higher syzygy of some positive codimensional module if and only if the ring is an integral domain. Also we discuss the hierarchy of rings with respect to Cohen–Macaulay approximation by codimensions of modules.
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Physical Sciences and Engineering
Mathematics
Algebra and Number Theory