On some properties of \(\oplus\)-supplemented modules.
type: Item
instance of: scholarly article
title: On some properties of \(\oplus\)-supplemented modules.
zbMATH Open document ID: 1066.16001
DOI: 10.1155/S016117120320346X
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2005-05-09T00:00:00Z
full work available at URL: https://eudml.org/doc/51433
review text: Summary: A module \(M\) is \(\oplus\)-supplemented if every submodule of \(M\) has a supplement which is a direct summand of \(M\). In this paper, we show that a quotient of a \(\oplus\)-supplemented module is not in general \(\oplus\)-supplemented. We prove that over a commutative ring \(R\), every finitely generated \(\oplus\)-supplemented \(R\)-module \(M\) having dual Goldie dimension less than or equal to three is a direct sum of local modules. It is also shown that a ring \(R\) is semisimple if and only if the class of \(\oplus\)-supplemented \(R\)-modules coincides with the class of injective \(R\)-modules. The structure of \(\oplus\)-supplemented modules over a commutative principal ideal ring is completely determined.
Mathematics Subject Classification ID: 16D70
Mathematics Subject Classification ID: 16D50
Mathematics Subject Classification ID: 13C13
zbMATH DE Number: 2166339
zbMATH Keywords: direct summands
zbMATH Keywords: \(\oplus\)-supplemented modules
zbMATH Keywords: finitely generated modules
zbMATH Keywords: direct sums
zbMATH Keywords: injective modules
zbMATH Keywords: commutative principal ideal rings
author: Abdelouahab Idelhadj
author: Rachid Tribak
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2166339