\(V\)-Gorenstein projective, injective and flat modules.
type: Item
instance of: scholarly article
title: \(V\)-Gorenstein projective, injective and flat modules.
zbMATH Open document ID: 1273.16010
DOI: 10.1216/RMJ-2012-42-6-2075
published in: Rocky Mountain Journal of Mathematics
publication date: 2013-04-09T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.rmjm/1361800619
review text: The main aim of the present paper is to study properties of \(V\)-Gorenstein projective, injective, respectively, flat modules. These results generalize some well known properties of projective, injective, respectively, flat modules. It is proved that the class of \(V\)-Gorenstein projective modules is closed with respect to kernels of epimorphisms (Theorem 2.3), direct sums and direct summands (Proposition 2.4), and if \(R\) is left perfect this class is closed with respect to direct limits of chains of \(V\)-Gorenstein projective modules. In Theorem 2.8 the authors provide a characterization for QF-rings using \(V\)-Gorenstein projective modules. Similar results are proved for \(V\)-Gorenstein injective, respectively, flat modules. For instance, it is proved that a left \(R\)-module \(M\) is \(V\)-Georenstein flat if and only if the dual \(M^+\) is \(V\)-Gorenstein injective (Theorem 3.3).
reviewed by: Simion Sorin Breaz
Mathematics Subject Classification ID: 16E30
Mathematics Subject Classification ID: 16E65
Mathematics Subject Classification ID: 16D40
Mathematics Subject Classification ID: 16D50
zbMATH DE Number: 6152199
zbMATH Keywords: \(V\)-Gorenstein projective modules
zbMATH Keywords: \(V\)-Gorenstein injective modules
zbMATH Keywords: \(V\)-Gorenstein flat modules
zbMATH Keywords: dualizing modules
Wikidata QID: Q114060102
author: Xiaoyan Yang
author: Zhongkui Liu
MaRDI profile type: Publication
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OpenAlex ID: W2028324204
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description: scientific article; zbMATH DE number 6152199