Generalized Krull domains and the composite semigroup ring \(D+E[\Gamma^{\ast}]\)
type: Item
instance of: scholarly article
title: Generalized Krull domains and the composite semigroup ring \(D+E[\Gamma^{\ast}]\)
zbMATH Open document ID: 1275.13001
author: Jung Wook Lim
published in: Journal of Algebra
publication date: 2012-11-09T00:00:00Z
review text: Let \(D\subseteq E\) be an extension of integral domains, let \(\Gamma\) be a nonzero torsion free additive grading monoid with quotient group \(G\) such that \(\Gamma \cap {-\Gamma}=\{0\}\), and let \(R =D+E[{\Gamma}^*]\), where \({\Gamma}^*= {\Gamma} \backslash \{0\} \). Under the assumption that \(G \) satisfies the ascending chain condition on cyclic subgroups, the author proves the following results: (i) \(R\) is generalized Krull domain if and only if \(D=E\), \(D\) is a generalized Krull domain and \(\Gamma\) is a generalized Krull semigroup, and (ii) \(R\) is a generalized unique factorization domain if and only if \(D=E\), \(D\) is generalized unique factorization domain and \(\Gamma \) is a weakly factorial GCD-semigroup.
reviewed by: Vahap Erdogdu
Mathematics Subject Classification ID: 13A02
Mathematics Subject Classification ID: 13A15
Mathematics Subject Classification ID: 13F15
Mathematics Subject Classification ID: 13G05
zbMATH DE Number: 6104523
zbMATH Keywords: Krull Domain
zbMATH Keywords: unique factorization domain
zbMATH Keywords: GCD Domain
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2012.02.008
OpenAlex ID: W2031551565
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DOI: 10.1016/J.JALGEBRA.2012.02.008
description: scientific article; zbMATH DE number 6104523