Group identities on units of rings
type: Item
instance of: scholarly article
title: Group identities on units of rings
zbMATH Open document ID: 0811.16027
DOI: 10.1007/BF01189563
author: Eric Jespers
author: Antonio Giambruno
author: Angela Valenti
published in: Archiv der Mathematik
publication date: 1994-11-13T00:00:00Z
review text: Let \(A\) be an algebra over an infinite commutative domain \(R\), and let \(R^{-1} A\) be the ring of fractions with respect to the non-zero elements of \(R\). It is shown that all idempotents of \(R^{-1} A\) are central provided \(A\) is semiprime and its unit group \({\mathcal U}(A)\) satisfies a group identity. As an application we prove, as conjectured by B. Hartley, that the group ring \(RG\) satisfies a polynomial identity provided \({\mathcal U}(RG)\) satisfies a group identity and \(G\) is a \(p'\)- group, where \(p\) is the characteristic of \(R\).
Mathematics Subject Classification ID: 16U60
Mathematics Subject Classification ID: 16S34
Mathematics Subject Classification ID: 16R50
Mathematics Subject Classification ID: 20C07
zbMATH DE Number: 687021
zbMATH Keywords: ring of fractions
zbMATH Keywords: idempotents
zbMATH Keywords: group identity
zbMATH Keywords: group ring
zbMATH Keywords: polynomial identity
zbMATH Keywords: \(p'\)-group
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01189563
OpenAlex ID: W1996728686
description: scientific article; zbMATH DE number 687021