Minimal injective resolutions of Cohen-Macaulay isolated singularities
type: Item
instance of: scholarly article
title: Minimal injective resolutions of Cohen-Macaulay isolated singularities
zbMATH Open document ID: 0967.13020
author: Shiro Goto
author: Kenji Nishida
published in: Archiv der Mathematik
publication date: 2001-08-23T00:00:00Z
review text: This paper studies (not necessarily commutative) finitely generated algebras \(\Lambda\) over a Gorenstein complete local ring \((R, {\mathfrak m})\) which are Cohen-Macaulay isolated singularities and finitely generated \(\Lambda\)-modules \(M\) which are Cohen-Macaulay \(R\)-modules with \(\dim_R M = \dim R\). The main result is a description of the minimal injective resolution of \(M\) in terms of the Cousin complex of \(M\) (as an \(R\)-module) and the minimal projective resolution of the \(R\)-dual of \(M\). As a consequence, the authors prove that if \(R\) is a regular local ring, \(\Lambda\) is \(k\)-Gorenstein if and only if the ring \((R/{\mathfrak m})\otimes_R\Lambda\) is \((k-\dim R)\)-Gorenstein. These results generalize earlier results of \textit{H. Fujita} [Commun. Algebra 26, No. 2, 447-451 (1998; Zbl 0895.16006)]. The paper concludes with several examples of Cohen-Macaulay isolated singularities.
reviewed by: Trung Ngo Viet
Mathematics Subject Classification ID: 13H10
Mathematics Subject Classification ID: 13D25
Mathematics Subject Classification ID: 13E05
Mathematics Subject Classification ID: 16E65
Mathematics Subject Classification ID: 13C14
Mathematics Subject Classification ID: 13D02
zbMATH DE Number: 1394462
zbMATH Keywords: minimal injective resolution
zbMATH Keywords: isolated singularity
zbMATH Keywords: Gorenstein ring
zbMATH Keywords: Cousin complex
MaRDI profile type: Publication
full work available at URL: s000130050394
OpenAlex ID: W2064636822
Wikidata QID: Q114232159
DOI: 10.1007/S000130050394
description: scientific article; zbMATH DE number 1394462