On Gorenstein injectivity of top local cohomology modules
type: Item
instance of: scholarly article
title: On Gorenstein injectivity of top local cohomology modules
zbMATH Open document ID: 1251.13017
DOI: 10.1090/S0002-9939-2011-11059-1
author: Takeshi Yoshizawa
published in: Proceedings of the American Mathematical Society
publication date: 2012-05-29T00:00:00Z
Mathematics Subject Classification ID: 13D45
Mathematics Subject Classification ID: 13D05
zbMATH DE Number: 6038822
zbMATH Keywords: local cohomology
zbMATH Keywords: Gorenstein injective module
Wikidata QID: Q122928672
MaRDI profile type: Publication
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full work available at URL: s0002-9939-2011-11059-1
OpenAlex ID: W2171499527
review text: Let \((R, \mathfrak m)\) be a \(d\)-dimensional commutative noetherian local ring and \(J\) be an ideal. The paper studies Gorenstein-injectivity of the top local cohomology module \(H^{d}_{J}(R)\). For example over complete hypersurface the author shows that \(H^{d}_{J}(R)\) is Gorenstein-injective. An example of the paper states that the hypersurface assumption is really needed. An auxiliary method is a torsion theory defined by a pair of ideals. Over a complete Cohen-Macaulay ring \((R, \mathfrak m)\), the Gorenstein-injectivity of \(H^{d}_{\mathfrak m}(R)\) is equivalent with the injectivity of \(H^{d}_{\mathfrak m}(R)\).
reviewed by: Mohsen Asgharzadeh
description: scientific article; zbMATH DE number 6038822