\(\mathcal A\)-projective modules and the injective dimension of cyclic torsionless modules.
type: Item
instance of: scholarly article
title: \(\mathcal A\)-projective modules and the injective dimension of cyclic torsionless modules.
zbMATH Open document ID: 1200.16004
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 2010-01-07T00:00:00Z
review text: The author introduces and studies the concept of \(\mathcal A\)-projective module. Thus, a module \(M\) is called \(\mathcal A\)-projective if \(\text{Ext}^1_R(M,R/I)=0\) for any left annihilator \(I\) in \(R\). He also defines a dimension which measures how far away a ring is from being left self-injective von Neumann regular. Precisely, this left dimension of \(R\) is given as the supremum of all injective dimensions of cyclic torsionless left \(R\)-modules.
reviewed by: Iuliu Crivei
Mathematics Subject Classification ID: 16D40
Mathematics Subject Classification ID: 16E10
Mathematics Subject Classification ID: 16E50
zbMATH DE Number: 5654590
zbMATH Keywords: generalized projective modules
zbMATH Keywords: left self-injective von Neumann regular rings
zbMATH Keywords: injective dimension
zbMATH Keywords: annihilators
author: Lixin Mao
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5654590