Unique factorization properties in commutative monoid rings with zero divisors
type: Item
instance of: scholarly article
title: Unique factorization properties in commutative monoid rings with zero divisors
zbMATH Open document ID: 1505.13027
author: J. R. Juett
author: Rhys D. Roberts
author: Christopher P. Mooney
published in: Semigroup Forum
publication date: 2021-06-09T00:00:00Z
review text: The authors defined and studied several different versions of ``factoriality'' for commutative rings with zero divisors. They provided necessary and sufficient conditions for a commutative monoid ring \(R[S]\) to be various kinds of ``unique factorization rings''. Their work generalizes Anderson et al.'s results about ``unique factorization'' in the polynomial ring \(R[X]\), Gilmer and Parker's characterization of factorial monoid domains, and Hardy and Shores's classification of when \(R[S]\) is a principal ideal ring (where \(S\) is a cancellative monoid). Also they studied when the monoid ring \(R[S]\) is ``restricted cancellative'' or satisfies various ``(restricted) ideal cancellation laws''.
reviewed by: Mohamed Khalifa
Mathematics Subject Classification ID: 13F15
Mathematics Subject Classification ID: 13A05
Mathematics Subject Classification ID: 13A15
Mathematics Subject Classification ID: 13F10
Mathematics Subject Classification ID: 20M25
zbMATH DE Number: 7357025
zbMATH Keywords: unique factorization rings with zero divisors
zbMATH Keywords: monoid ring
zbMATH Keywords: restricted cancellative ring
zbMATH Keywords: (restricted) ideal cancellation laws
zbMATH Keywords: principal ideal ring
MaRDI profile type: Publication
full work available at URL: s00233-020-10154-x
OpenAlex ID: W3152421003
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DOI: 10.1007/S00233-020-10154-X
description: scientific article; zbMATH DE number 7357025