On weakly periodic-like rings and commutativity.
type: Item
instance of: scholarly article
title: On weakly periodic-like rings and commutativity.
zbMATH Open document ID: 1123.16022
author: Adil Yaqub
published in: Results in Mathematics
publication date: 2007-02-15T00:00:00Z
review text: Let \(R\) be a ring; and let \(Z\), \(J\), \(E\) and \(N\) denote respectively the center, the Jacobson radical, the set of idempotents, and the set of nilpotent elements. Let \(p\) be a fixed prime. Define \(R\) to be an \(N_0\)-ring if for each \(x,y\in R\setminus(N\cup J\cup Z)\) there exists \(n=n(x,y)>1\) for which \(x^ny-xy^n\in N\); and if, in addition, \(pR=\{0\}\) and all \(n(x,y)\) can be taken as \(p\), call \(R\) a generalized \(p\)-ring. The author studies commutativity in \(N_0\)-rings and generalized \(p\)-rings with additional properties. A typical theorem states that a generalized \(p\)-ring with 1 must be commutative if \(J\) is commutative and \(E\subseteq Z\).
Mathematics Subject Classification ID: 16U80
Mathematics Subject Classification ID: 16U70
zbMATH DE Number: 5127420
zbMATH Keywords: weakly periodic-like rings
zbMATH Keywords: generalized \(p\)-rings
zbMATH Keywords: commutativity theorems
zbMATH Keywords: idempotents
zbMATH Keywords: nilpotent elements
MaRDI profile type: Publication
full work available at URL: s00025-006-0230-4
OpenAlex ID: W2158398419
DOI: 10.1007/S00025-006-0230-4
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description: scientific article; zbMATH DE number 5127420