Almost QF rings and almost \(\text{QF}^ \#\) rings
type: Item
instance of: scholarly article
title: Almost QF rings and almost \(\text{QF}^ \#\) rings
zbMATH Open document ID: 0807.16003
author: Manabu Harada
published in: Osaka Journal of Mathematics
publication date: 1994-07-12T00:00:00Z
review text: The author has defined almost projective modules and almost injective modules [in J. Algebra 159, 150-157 (1993; Zbl 0795.16003)]. Let \(R\) be a two-sided artinian ring with identity. The author calls \(R\) a right almost QF ring in case \(R\) is almost injective as a right \(R\)-module, and calls \(R\) a right almost \(\text{QF}^ \#\) ring in case every right injective \(R\)-module is almost projective. The main result states that \(R\) is right almost QF (almost \(\text{QF}^ \#\)) if and only if \(R\) is a right co-\(H\) ring (\(H\)-ring), i.e., every non-cosmall right \(R\)-module contains a projective direct summand (every non-small right \(R\)-module contains a non-zero injective module).
Mathematics Subject Classification ID: 16D40
Mathematics Subject Classification ID: 16P20
Mathematics Subject Classification ID: 16D50
Mathematics Subject Classification ID: 16L60
Mathematics Subject Classification ID: 16D70
zbMATH DE Number: 591444
zbMATH Keywords: almost projective modules
zbMATH Keywords: almost injective modules
zbMATH Keywords: two-sided artinian ring
zbMATH Keywords: right almost QF ring
zbMATH Keywords: right almost \(\text{QF}^ \#\) ring
zbMATH Keywords: right co-\(H\) ring
zbMATH Keywords: projective direct summand
reviewed by: Xue Weimin
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 591444