Extensions of reversible rings.
type: Item
instance of: scholarly article
title: Extensions of reversible rings.
zbMATH Open document ID: 1040.16021
DOI: 10.1016/S0022-4049(03)00109-9
author: Nam Kyun Kim
author: Yang Lee
published in: Journal of Pure and Applied Algebra
publication date: 2003-11-19T00:00:00Z
review text: A ring \(R\) is called reversible if \(ab = 0\) implies \(ba = 0\) for \(a,b\) \(\in R\). Some authors call this ring zero-commutative. The authors obtain some basic properties of basic extensions of these rings. Let \(T(R,R)\) and \(R[x]\) be the \(2\) by \(2\) upper triangular matrix ring and polynomial ring over \(R\), respectively. If \(R\) is reduced (i.e., there are no non-zero nilpotent elements in \(R\)), the authors prove that \(T(R,R)\) and \(R[x]/ (x^n)\) are reversible rings, where \((x^n)\) is the ideal of \(R[x]\) generated by \(x^n\).
Mathematics Subject Classification ID: 16U80
Mathematics Subject Classification ID: 16U10
Mathematics Subject Classification ID: 16U20
zbMATH DE Number: 2005928
zbMATH Keywords: reversible rings
zbMATH Keywords: zero-commutative rings
zbMATH Keywords: reduced rings
reviewed by: Xue Weimin
MaRDI profile type: Publication
cites work: Armendariz rings and gaussian rings
cites work: Semigroups and rings whose zero products commute
cites work: A note on extensions of Baer and P. P. -rings
cites work: Reversible Rings
cites work: Q4198895
cites work: ARMENDARIZ RINGS AND SEMICOMMUTATIVE RINGS
cites work: Armendariz rings and reduced rings
cites work: Q4113971
cites work: On the Representation of Modules by Sheaves of Factor Modules
cites work: Q3786586
cites work: Q5735274
cites work: Armendariz rings
cites work: Prime Ideals and Sheaf Representation of a Pseudo Symmetric Ring
full work available at URL: s0022-4049(03)00109-9
OpenAlex ID: W2027895850
description: scientific article; zbMATH DE number 2005928