Commuting idempotents, square-free modules, and the exchange property.
type: Item
instance of: scholarly article
title: Commuting idempotents, square-free modules, and the exchange property.
zbMATH Open document ID: 1337.16008
author: Ryszard Mazurek
author: Pace P. Nielsen
author: Michał Ziembowski
published in: Journal of Algebra
publication date: 2015-10-13T00:00:00Z
review text: The paper has three main results. Firstly, a criterion is obtained for when idempotents of a ring \(R\) which commute modulo the Jacobson radical \(J(R)\) can be lifted to commuting idempotents of \(R\). Secondly, it is proved that if \(R/J(R)\) is an internal exchange ring and idempotents lift modulo \(J(R)\), then \(R\) is an internal exchange ring. Lastly, the authors establish and clarify inclusion relations between square-free modules, modules with (finite) exchange property, modules with \(C_3\) property, and modules that possess other related properties.
reviewed by: David Ssevviiri
Mathematics Subject Classification ID: 16D70
Mathematics Subject Classification ID: 16N20
Mathematics Subject Classification ID: 16U80
zbMATH DE Number: 6493619
zbMATH Keywords: commuting idempotents
zbMATH Keywords: half-commuting idempotents
zbMATH Keywords: internal exchange property
zbMATH Keywords: lifting idempotents
zbMATH Keywords: square-free modules
zbMATH Keywords: \(C_3\) property
zbMATH Keywords: exchange rings
zbMATH Keywords: direct sums
zbMATH Keywords: finite exchange property
zbMATH Keywords: direct summands
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2015.07.015
OpenAlex ID: W1161458362
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DOI: 10.1016/J.JALGEBRA.2015.07.015
description: scientific article; zbMATH DE number 6493619