Strongly injective modules
type: Item
instance of: scholarly article
title: Strongly injective modules
zbMATH Open document ID: 1471.16005
author: Ergül Türkmen
author: Burcu Nişancı Türkmen
publication date: 2021-05-04T00:00:00Z
review text: Let \(R\) be a ring with unity and \(M\) be a left \(R\)-module. In this paper, a module \(M\) is called strongly injective if whenever \(M+K=N\) with \(M\leq N\), there exists \(L\leq K\) such that \(M\oplus L=N\). Then the authors show that a module is strongly injective if and only if it is semisimple and injective. Further, new characterizations of left V-rings and semisimple rings are given via strongly injective modules. In particular, it is shown that \(R\) is a left V-ring if and only if every Artinian left \(R\)-module is strongly injective. Also it is shown that a ring \(R\) is semisimple if and only if every left \(R\)-module is strongly injective.
Mathematics Subject Classification ID: 16D10
Mathematics Subject Classification ID: 16D50
Mathematics Subject Classification ID: 16K99
zbMATH DE Number: 7343247
zbMATH Keywords: strongly injective module
zbMATH Keywords: semisimple ring
zbMATH Keywords: left V-ring
Wikidata QID: Q114221103
reviewed by: Jae Keol Park
MaRDI profile type: Publication
full work available at URL: s12215-019-00479-0
OpenAlex ID: W2996831651
cites work: Strongly noncosingular modules
cites work: Q4056148
cites work: Extensions of weakly supplemented modules
cites work: Q5471610
cites work: Q3166698
cites work: Small Modules
cites work: On small and cosmall modules
cites work: Q5656860
cites work: Finitely generated supplemented modules are amply supplemented.
cites work: Q4534148
cites work: Q4002547
cites work: Moduln, die in jeder Erweiterung ein Komplement haben.
DOI: 10.1007/S12215-019-00479-0
published in: Rendiconti del Circolo Matematico di Palermo
description: scientific article; zbMATH DE number 7343247