Commutativity of rings with constraints on nilpotents and nonnilpotents
type: Item
instance of: scholarly article
title: Commutativity of rings with constraints on nilpotents and nonnilpotents
zbMATH Open document ID: 0678.16026
DOI: 10.1155/S0161171289000591
author: Mohamad Hasanali
author: Adil Yaqub
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/46397
review text: Let R be a ring, N its set of nilpotent elements, and \(n>1\) a fixed positive integer. It is proved that R is commutative if it satisfies the following conditions: (i) N is commutative; (ii) \(x^ ny=xy^ n\) for all \(x,y\in R\setminus N\); (iii) if \(a\in N\), \(b\in R\) and \(n![a,b]=0\), then \([a,b]=0\). None of the three conditions can be deleted.
Mathematics Subject Classification ID: 16U70
zbMATH DE Number: 4110887
zbMATH Keywords: nonnilpotents
zbMATH Keywords: nilpotent elements
zbMATH Keywords: commutative
MaRDI profile type: Publication
OpenAlex ID: W1983186861
description: scientific article; zbMATH DE number 4110887