Closed weak supplemented modules.
type: Item
instance of: scholarly article
title: Closed weak supplemented modules.
zbMATH Open document ID: 1127.16004
author: Qingyi Zeng
published in: Vietnam Journal of Mathematics
publication date: 2007-01-31T00:00:00Z
review text: A module \(M\) is called closed weak supplemented if for any closed submodule \(N\) of \(M\), there is a submodule \(K\) of \(M\) such that \(M=N+K\) and \(K\cap N\) is small in \(N\). Several properties of closed weak supplemented modules are studied. For example, any direct summand of a closed weak supplemented module is also closed weak supplemented. A ring \(R\) is closed weak supplemented if the module \(R_R\) is closed weak supplemented. It is shown that a ring \(R\) is closed weak supplemented if and only if the \(n\)-by-\(n\) matrix ring \(M_n(R)\) over \(R\) is closed weak supplemented for any positive integer \(n\).
reviewed by: Jae Keol Park
Mathematics Subject Classification ID: 16D70
Mathematics Subject Classification ID: 16S50
zbMATH DE Number: 5120081
zbMATH Keywords: closed submodules
zbMATH Keywords: closed weak supplemented submodules
zbMATH Keywords: small submodules
zbMATH Keywords: direct summands
zbMATH Keywords: nonsingular modules
zbMATH Keywords: essential submodules
zbMATH Keywords: matrix rings
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5120081