Gorenstein modules, finite index, and finite Cohen-Macaulay type

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Abstract

A Gorenstein module over a local ring R is a maximal Cohen-Macaulay module of finite injective dimension. We use existence of Gorenstein modules to extend a result due to S. Ding: A Cohen-Macaulay ring of finite index, with a Gorenstein module, is Gorenstein on the punctured spectrum. We use this to show that a Cohen-Macaulay local ring of finite Cohen-Macaulay type is Gorenstein on the punctured spectrum. Finally, we show that for a large class of rings (including all excellent rings), the Gorenstein locus of a finitely generated module is an open set in the Zariski topology.

Original languageEnglish (US)
Pages (from-to)2023-2035
Number of pages13
JournalCommunications in Algebra
Volume30
Issue number4
DOIs
StatePublished - Apr 2002
Externally publishedYes

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ASJC Scopus subject areas

  • Algebra and Number Theory

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