Syzygies of modules with positive codimension
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- 作者：Kiriko Kato
- 关键词：Cohen– ; Macaulay approximation ; Cohen– ; Macaulay module
- 刊名：Journal of Algebra
- 出版年：2007
- 出版时间：1 December 2007
- 年：2007
- 卷：318
- 期：1
- 页码：25-36
- 全文大小：153 K
文摘
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.