Associate elements in commutative rings
type: Item
instance of: scholarly article
title: Associate elements in commutative rings
zbMATH Open document ID: 1302.13001
DOI: 10.1216/RMJ-2014-44-3-717
author: Sangmin Chun
author: D. D. Anderson
published in: Rocky Mountain Journal of Mathematics
publication date: 2014-09-30T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.rmjm/1411945660
review text: This paper deals with several kinds of associateness of elements in commutative rings, and the connections between them. For example, in this paper, two elements \(a\) and \(b\) in a commutative ring \(R\) are called \textit{associates} if \(aR=bR\). The ring \(R\) is \textit{strongly associate} if for two associate elements \(a\) and \(b\), we have \(a=ub \) for a unit \(u\in R\). The authors define and study \textit{strongly regular associate rings}, they deal also with presimpliable rings (defined by A. Bouvier), etc. They relate associateness properties to other ring properties as, e.g., the bounded factorization property. The authors investigate stability of the various properties with respect to direct products, ultraproducts, etc. They also include many relevant examples.
reviewed by: Moshe Roitman
Mathematics Subject Classification ID: 13A05
Mathematics Subject Classification ID: 13F15
zbMATH DE Number: 6349606
zbMATH Keywords: associate elements
zbMATH Keywords: presimplifiable rings
zbMATH Keywords: strongly associate rings
zbMATH Keywords: strongly regular associates
MaRDI profile type: Publication
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OpenAlex ID: W2019173470
description: scientific article; zbMATH DE number 6349606