On derivations and commutativity in prime rings
type: Item
instance of: scholarly article
title: On derivations and commutativity in prime rings
zbMATH Open document ID: 0822.16033
DOI: 10.1007/BF01876049
published in: Acta Mathematica Hungarica
publication date: 1995-08-30T00:00:00Z
review text: Let \(R\) be a prime ring, \(U\) be a right ideal of \(R\), and \(d\) be a nonzero derivation of \(R\). It is shown that each of the following three conditions (i) \([d(x),d(y)] = d([y,x])\) for all \(x,y\in R\), (ii) \([d(x),d(y)] = d([x,y])\) for all \(x,y\in R\), (iii) \(\text{char\,}R\neq 2\) and \(d([x,y]) = 0\) for all \(x,y\in R\), implies that either \(R\) is commutative or \(d^ 2(U) = d(U)^ 2 = \{0\}\).
Mathematics Subject Classification ID: 16W25
Mathematics Subject Classification ID: 16N60
Mathematics Subject Classification ID: 16U70
Mathematics Subject Classification ID: 16U80
zbMATH DE Number: 755487
zbMATH Keywords: commutativity theorems
zbMATH Keywords: prime rings
zbMATH Keywords: right ideals
zbMATH Keywords: derivations
author: Howard E. Bell
author: M. Nagy Daif
reviewed by: Matej Brešar
MaRDI profile type: Publication
cites work: Centralizing Mappings of Semiprime Rings
cites work: Rings in which derivations satisfy certain algebraic conditions
cites work: On Commutativity and Strong Commutativity-Preserving Maps
cites work: Remarks on derivations on semiprime rings
cites work: A Note on Derivations
cites work: Derivations in Prime Rings
full work available at URL: https://doi.org/10.1007/bf01876049
OpenAlex ID: W3094304795
description: scientific article; zbMATH DE number 755487