Direct sums and summands of weak CS-modules and continuous modules
type: Item
instance of: scholarly article
title: Direct sums and summands of weak CS-modules and continuous modules
zbMATH Open document ID: 0942.16008
author: Noyan Er
published in: Rocky Mountain Journal of Mathematics
publication date: 2000-05-28T00:00:00Z
full work available at URL: CONT29-2.html
review text: A module \(M\) is called a weak CS-module if every semisimple submodule of \(M\) is essential in a direct summand of \(M\). In this paper, the author studies the question of when direct sums and direct summands of weak CS-modules are weak CS-modules. It is shown, in particular, that a finite direct sum of relatively injective weak CS-modules is again weak CS. The author defines a module \(M\) to be a weak \(C_{11}\)-module if every semisimple submodule has a complement in \(M\) which is a direct summand of \(M\), and he shows that any direct sum of weak CS-modules is a weak \(C_{11}\)-module. Finally, some characterizations of continuous modules are given.
reviewed by: Nguyen Viet Dung
Mathematics Subject Classification ID: 16D80
Mathematics Subject Classification ID: 16D70
Mathematics Subject Classification ID: 16D50
Mathematics Subject Classification ID: 16D60
zbMATH DE Number: 1356453
zbMATH Keywords: weak CS-modules
zbMATH Keywords: direct sums
zbMATH Keywords: continuous modules
zbMATH Keywords: direct summands
zbMATH Keywords: semisimple modules
zbMATH Keywords: relatively injective modules
MaRDI profile type: Publication
OpenAlex ID: W1988731506
cites work: Q4843160
cites work: Q4288191
cites work: Q3674835
cites work: Q3995216
cites work: Q3199588
cites work: Q4891439
cites work: Q4020717
cites work: Generalizations of CS-modules
DOI: 10.1216/RMJM/1181071648
description: scientific article; zbMATH DE number 1356453