Forcing linearity numbers for modules over rings with nontrivial idempotents
type: Item
instance of: scholarly article
title: Forcing linearity numbers for modules over rings with nontrivial idempotents
zbMATH Open document ID: 1015.16035
DOI: 10.1016/S0021-8693(02)00128-X
published in: Journal of Algebra
publication date: 2003-02-12T00:00:00Z
review text: Let \(R\) be a ring and \(V\) an \(R\) module. All rings in this paper are associative, have an identity 1, and all modules are unital. The authors determine forcing linearity numbers of \(V\) in terms of certain modules over the rings \(e_iRe_i\). If each \(e_iRe_i\) is a division ring they obtain precise answers. They find the forcing linearity numbers for all modules over Artinian rings. The paper is divided into the sections of Introduction; General Results; Determination of Forcing Linear Numbers; Applications and Remarks; and Forcing Linearity Numbers over Artinian Rings. In the last section, instead of focusing on properties of the decomposition of the modules \(e_iV\), they focus on properties of the rings \(e_iRe_i\).
Mathematics Subject Classification ID: 16S50
Mathematics Subject Classification ID: 16Y30
Mathematics Subject Classification ID: 16P20
Mathematics Subject Classification ID: 16D10
zbMATH DE Number: 1868021
zbMATH Keywords: formal matrix rings
zbMATH Keywords: forcing linearity numbers
zbMATH Keywords: modules over Artinian rings
author: C. J. Maxson
author: A. B. van der Merwe
reviewed by: Yueh-er Kuo
MaRDI profile type: Publication
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full work available at URL: s0021-8693(02)00128-x
OpenAlex ID: W1976040098
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description: scientific article; zbMATH DE number 1868021