Remarks on reflexive modules, covers, and envelopes
type: Item
instance of: scholarly article
title: Remarks on reflexive modules, covers, and envelopes
zbMATH Open document ID: 1186.13004
published in: Beiträge zur Algebra und Geometrie
publication date: 2009-09-02T00:00:00Z
full work available at URL: https://eudml.org/doc/229036
full work available at URL: 5.html
review text: The author presents results on reflexive modules over Gorenstein rings which generalize results of Serre and Samuel on reflexive modules over regular local rings. The Gorenstein rings of dimension at most two are characterized by the property that the dual module \(\Hom_R(M, R)\) has G-dimension zero for every finitely generated \(R\)-module \(M\). In the second section, the notions of a reflexive cover and a reflexive envelope of a module are introduced and the author shows that every finitely generated \(R\)-module has a reflexive cover, if \(R\) is a Gorenstein local ring of dimension at most two. Finally, it is shown that every finitely generated \(R\)-module has a reflexive envelope, if \(R\) is quasi-normal or if \(R\) is locally an integral domain.
reviewed by: Marco Fontana
Mathematics Subject Classification ID: 13C13
Mathematics Subject Classification ID: 13H10
Mathematics Subject Classification ID: 13D05
Mathematics Subject Classification ID: 13C10
zbMATH DE Number: 5601571
zbMATH Keywords: reflexive module
zbMATH Keywords: cover
zbMATH Keywords: envelope
zbMATH Keywords: G-dimension
zbMATH Keywords: Gorenstein ring
author: Richard G. Belshoff
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5601571