GORENSTEIN MODULES, FINITE INDEX, AND FINITE COHEN–MACAULAY TYPE
| Autor: | Graham J. Leuschke |
|---|---|
| Rok vydání: | 2002 |
| Předmět: |
Large class
Discrete mathematics Pure mathematics Zariski topology Algebra and Number Theory Mathematics::Commutative Algebra Mathematics::Rings and Algebras Open set Local ring Injective function Mathematics::Algebraic Geometry Cohen–Macaulay ring Finitely-generated module Locus (mathematics) Mathematics |
| Zdroj: | Communications in Algebra. 30:2023-2035 |
| ISSN: | 1532-4125 0092-7872 |
| DOI: | 10.1081/agb-120013229 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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