The Jacobson radical of commutative semigroup rings
type: Item
instance of: scholarly article
title: The Jacobson radical of commutative semigroup rings
zbMATH Open document ID: 0772.16012
DOI: 10.1016/S0021-8693(05)80037-7
published in: Journal of Algebra
publication date: 1993-03-29T00:00:00Z
review text: Let \(R[S]\) be a commutative semigroup ring. The author gives another description of the Jacobson radical of \(R[S]\) which yields necessary and sufficient conditions on \(R\) and \(S\) for the Jacobson radical and prime radical of \(R[S]\) to coincide. This in turn yields necessary and sufficient conditions for \(R[S]\) to be semiprimitive. These results recover several special cases of W. D. Munn.
reviewed by: David F. Anderson
Mathematics Subject Classification ID: 16S36
Mathematics Subject Classification ID: 20M25
Mathematics Subject Classification ID: 16N20
Mathematics Subject Classification ID: 16D60
Mathematics Subject Classification ID: 13A10
zbMATH DE Number: 130639
zbMATH Keywords: semiprimitive rings
zbMATH Keywords: commutative semigroup ring
zbMATH Keywords: Jacobson radical
zbMATH Keywords: prime radical
author: A. V. Kelarev
MaRDI profile type: Publication
cites work: Q3848243
cites work: The Jacobson radical of semigroup rings of commutative semigroups
cites work: The Brown Mccoy radical of semigroup rings of commutative cancellative semigroups
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cites work: Q3729095
full work available at URL: s0021-8693(05)80037-7
OpenAlex ID: W2094650336
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description: scientific article; zbMATH DE number 130639