On CLS-modules
type: Item
instance of: scholarly article
title: On CLS-modules
zbMATH Open document ID: 0848.16006
author: A. Tercan
published in: Rocky Mountain Journal of Mathematics
publication date: 1996-08-05T00:00:00Z
review text: Let \(M\) be an \(R\)-module. A submodule \(K\) of \(M\) is defined to be closed if \(M/K\) is non-singular, and \(M\) is a CLS-module if every closed submodule of \(M\) is a direct summand of \(M\). The concept of a CLS-module generalises that of a CS-module, but the concepts coincide for non-singular modules. The direct sum of two CLS-modules need not be a CLS-module. The main result of this paper is that a finite direct sum of relatively injective CLS-modules is a CLS-module.
Mathematics Subject Classification ID: 16D50
Mathematics Subject Classification ID: 16D70
Mathematics Subject Classification ID: 16D10
zbMATH DE Number: 894666
zbMATH Keywords: closed submodules
zbMATH Keywords: direct summands
zbMATH Keywords: CS-modules
zbMATH Keywords: non-singular modules
zbMATH Keywords: direct sums
zbMATH Keywords: CLS-modules
zbMATH Keywords: relatively injective CLS-modules
reviewed by: A. W. Chatters
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/rmjm/1181072161
OpenAlex ID: W2079046794
cites work: Q4056148
cites work: RINGS IN WHICH EVERY COMPLEMENT RIGHT IDEAL IS A DIRECT SUMMAND
cites work: Endomorphism Rings of Modules over non-singular CS Rings
cites work: Q4288191
cites work: Extending modules over commutative domains
cites work: Q3995216
cites work: Nonsingular Rings
cites work: Q3199588
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cites work: Generalizations of CS-modules
DOI: 10.1216/RMJM/1181072161
description: scientific article; zbMATH DE number 894666