On the multiplicative semigroup of a ring
type: Item
instance of: scholarly article
title: On the multiplicative semigroup of a ring
zbMATH Open document ID: 0961.20055
DOI: 10.1007/BF02773220
published in: Israel Journal of Mathematics
publication date: 2000-09-19T00:00:00Z
review text: The authors prove that if \(R\) is a PI-ring and if the multiplicative semigroup of \(R\) is finitely generated then \(R\) must be finite. Note that it is well known that if \(R\) is commutative and infinite its multiplicative semigroup is not finitely generated. Whether this is the case or not, for general associative rings, is still an open question.
Mathematics Subject Classification ID: 20M25
Mathematics Subject Classification ID: 16R99
Mathematics Subject Classification ID: 16S15
Mathematics Subject Classification ID: 16P10
zbMATH DE Number: 1445782
zbMATH Keywords: multiplicative semigroups of rings
zbMATH Keywords: finitely generated multiplicative semigroups
zbMATH Keywords: PI-rings
zbMATH Keywords: finiteness theorems
author: A. Klein
author: Howard E. Bell
reviewed by: Plamen Koshlukov
MaRDI profile type: Publication
cites work: The nilpotency of the radical in a finitely generated P.I. ring
cites work: Q3934450
cites work: On the Multiplicative Semigroup of a Commutative Ring
full work available at URL: https://doi.org/10.1007/bf02773220
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description: scientific article; zbMATH DE number 1445782