Divisibility properties related to star-operations on integral domains
type: Item
instance of: scholarly article
zbMATH Open document ID: 1258.13002
author: Mi Hee Park
author: Francesca Tartarone
publication date: 2012-10-25T00:00:00Z
full work available at URL: 5-V12-2012.pdf
Mathematics Subject Classification ID: 13A05
Mathematics Subject Classification ID: 13A15
Mathematics Subject Classification ID: 13F05
Mathematics Subject Classification ID: 13G05
zbMATH DE Number: 6098603
zbMATH Keywords: \(GCD\)
zbMATH Keywords: star operation
MaRDI profile type: Publication
title: Divisibility properties related to star-operations on integral domains
published in: International Electronic Journal of Algebra (IEJA)
review text: The authors introduce and study the notion of \(GCD\)-Bézout domains. A domain \(R\) is called a \(GCD\)-Bézout domain if the Bézout identity holds for any set of nonzero elements of \(R\) whose \(\mathrm{gcd}\) exists. Among others, they characterize \(GCD\)-Bézout domains as \(DW\)-domains (i. e., the \(w\)-operation is trivial, or \(w=d\)) having the \(PSP\)-property (that is, each primitive ideal is superprimitive). They also introduced a new (semi)-star operation called the \(\tilde{p}\)-operation and used it to give another characterization of \(GCD\)-Bézout domains. It turns out that a domain is a \(GCD\)-Béezout domain if and only if \(\tilde{p}=d\) as star operation.
reviewed by: A. Mimouni
description: scientific article; zbMATH DE number 6098603