Modules of \(G\)-dimension zero over local rings of depth two
type: Item
instance of: scholarly article
title: Modules of \(G\)-dimension zero over local rings of depth two
zbMATH Open document ID: 1076.13007
author: Ryo Takahashi
published in: Illinois Journal of Mathematics
publication date: 2005-03-01T00:00:00Z
review text: Let \(R\) be a commutative Noetherian local ring. The concept of Gorenstein dimension of a module was introduced by Auslander and its finiteness characterizes the Gorenstein property of the ring. The main result of the paper under review proves that if \(R\) is a henselian non-Gorenstein local ring of depth two with a non-free \(R\)-module of \(G\)-dimension zero, then the category of modules of \(G\)-dimension zero, \({\mathcal G}(R)\), is not contravariantly finite in mod-\(R\), i.e. not every \(M\in \text{mod-}R\) has an \({\mathcal G}(R)\)-precover.
Mathematics Subject Classification ID: 13D05
Mathematics Subject Classification ID: 13H10
Mathematics Subject Classification ID: 13J15
zbMATH DE Number: 2140258
zbMATH Keywords: Gorenstein dimension
zbMATH Keywords: precover
zbMATH Keywords: henselian ring
reviewed by: Blas Torrecillas
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2140258