Localizations of tensor products.
type: Item
instance of: scholarly article
title: Localizations of tensor products.
zbMATH Open document ID: 1304.20067
DOI: 10.4171/RSMUP/131-14
author: Manfred Dugas
author: Kelly Aceves
author: Bradley Wagner
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 2014-08-13T00:00:00Z
review text: Let \(A\) and \(B\) be modules. A homomorphism \(\lambda\colon A\to B\) is called a localization if for all \(\varphi\in\Hom(A,B)\) there is a unique \(\psi\in\Hom(B,B)\) such that \(\varphi=\psi\circ\lambda\). The authors investigate localizations of tensor products of torsion-free Abelian groups. For example, they show that if \(R\) is a torsion-free ring, the natural multiplication \(\mu\colon R\otimes R\to R\) is a localization if and only if \(R\) is an \(E\)-ring. Their results are applied to present some surprising properties of tensor powers of torsion-free Abelian groups, for example strongly indecomposable groups \(G\) for which \(G\otimes G\) is reduced and completely decomposable.
reviewed by: Phillip Schultz
Mathematics Subject Classification ID: 20K30
Mathematics Subject Classification ID: 20K20
Mathematics Subject Classification ID: 16S50
Mathematics Subject Classification ID: 16W20
zbMATH DE Number: 6329767
zbMATH Keywords: torsion-free Abelian groups
zbMATH Keywords: tensor products
zbMATH Keywords: localizations
zbMATH Keywords: strongly indecomposable groups
zbMATH Keywords: \(E\)-rings
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 6329767