A generalization of projective covers
type: Item
instance of: scholarly article
title: A generalization of projective covers
zbMATH Open document ID: 1173.16002
author: Mustafa Alkan
author: W. Keith Nicholson
author: A. Çiğdem Özcan
published in: Journal of Algebra
publication date: 2008-07-29T00:00:00Z
full work available at URL: http://hdl.handle.net/11655/19796
review text: The authors generalize the notion of a projective cover of a module to the projective \(I\)-cover of a module for an ideal \(I\) of a ring \(R\). They prove that a ring \(R\) is \(I\)-semiregular if and only if every cyclically presented \(R\)-module has a projective \(I\)-cover. Using this they derive equivalent conditions for a ring \(R\) to be \(Z(_RR)\)-semiregular and \(\text{Soc}(_RR)\)-semiregular. Then they study \(I\)-semiperfect modules. They prove that a ring \(R\) is \(I\)-semiperfect if and only if every simple factor module of \(_RR\) has projective \(I\)-cover. As a corollary they get equivalent conditions for a ring \(R\) to be \(Z(_RR)\)-semiperfect. Finally they prove that a ring \(R\) is \(Z_2(_RR)\)-semiperfect if and only if every simple factor module of \(_RR\) has a projective \(Z_2(_RR)\)-semicover.
reviewed by: Veereshwar A. Hiremath
Mathematics Subject Classification ID: 16D40
Mathematics Subject Classification ID: 16E50
Mathematics Subject Classification ID: 16L30
zbMATH DE Number: 5304605
zbMATH Keywords: projective covers of modules
zbMATH Keywords: semiregular rings
zbMATH Keywords: semiperfect rings
zbMATH Keywords: projective \(I\)-covers
zbMATH Keywords: semiperfect modules
MaRDI profile type: Publication
OpenAlex ID: W2130100396
Wikidata QID: Q105368303
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DOI: 10.1016/J.JALGEBRA.2008.03.029
description: scientific article; zbMATH DE number 5304605