Rings over which polynomial rings are semi-commutative.
type: Item
instance of: scholarly article
title: Rings over which polynomial rings are semi-commutative.
zbMATH Open document ID: 1191.16025
author: Gang Yang
author: Ruijuan Du
published in: Vietnam Journal of Mathematics
publication date: 2010-01-13T00:00:00Z
full work available at URL: 527.htm
review text: A semi-commutative ring is a ring for which \(ab=0\) implies \(aRb=0\) for \(a,b\in R\). For such a ring \(R\), it is known that the polynomial ring \(R[x]\) need not be semi-commutative. The authors define and study strongly semi-commutative rings (SSC rings). By definition, this is a ring for which the associated polynomial ring will be semi-commutative. It is shown that the class of reversible rings (\(ab=0\) implies \(ba=0\)) is not comparable with that of the SSC rings. Construction techniques for SSC rings are given and a number of basic properties of these rings is established.
reviewed by: Stefan Veldsman
Mathematics Subject Classification ID: 16S36
Mathematics Subject Classification ID: 16U80
Mathematics Subject Classification ID: 16N60
zbMATH DE Number: 5656869
zbMATH Keywords: strongly semi-commutative rings
zbMATH Keywords: reversible rings
zbMATH Keywords: strongly Hopfian rings
zbMATH Keywords: SSC rings
zbMATH Keywords: polynomial rings
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5656869