Group rings and semigroup rings over strong Mori domains. II.
type: Item
instance of: scholarly article
title: Group rings and semigroup rings over strong Mori domains. II.
zbMATH Open document ID: 1106.13022
author: Mi Hee Park
published in: Journal of Algebra
publication date: 2004-10-01T00:00:00Z
review text: The concept of strong Mori domains was introduced by \textit{F. G. Wang} and \textit{R. L. McCasland} in [Commun. Algebra 25, 1285--1306 (1997; Zbl 0895.13010)] as a generalization of noetherian domains and Krull domains, which means an integral domain satisfying the ascending chain condition on \(w\)-ideals. The main aim of this paper is to characterize the condition under which the semigroup ring \(R[X;S]\) from an integral domain \(R\) and a torsion-free cancellative additive monoid \(S\) with quotient group \(G\) is a strong Mori semigroup. It is shown that \(R[X;S]\) is a strong Mori domain if and only if \(R\) is a strong Mori domain, \(S\) is a strong Mori semigroup and each nonzero element of \(G\) is of type \((0,0,\dots)\). [For Part I see J. Pure Appl. Algebra 163, No. 3, 301--318 (2001; Zbl 1094.13530).]
reviewed by: Fang Li
Mathematics Subject Classification ID: 13F05
Mathematics Subject Classification ID: 13A15
Mathematics Subject Classification ID: 16S36
zbMATH DE Number: 2105395
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2003.11.009
OpenAlex ID: W2013671012
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DOI: 10.1016/J.JALGEBRA.2003.11.009
description: scientific article; zbMATH DE number 2105395