On some properties of derivations on semiprime rings.
type: Item
instance of: scholarly article
title: On some properties of derivations on semiprime rings.
zbMATH Open document ID: 1109.16032
author: A. B. Thaheem
published in: Southeast Asian Bulletin of Mathematics
publication date: 2006-12-06T00:00:00Z
review text: Let \(R\) be a semiprime ring with center \(Z(R)\), and let \(f,g\colon R\to R\). Using easy computations, the author obtains some results when \(f\) and \(g\) are generalized inner derivations satisfying simple identities, and proves some technical commutativity results. Some of these are: when \(R\) is 2-torsion free and \(f(r)=ar+rb\) then \(f\) is a reverse derivation if and only if \(f=0\); if \(f\) and \(g\) are inner derivations so that \(f(x)x+xg(x)=0\) for all \(x\in R\) then \(f=g=0\); when \(f(r)=ar+rb\) and \(f(x)x=xf(x)\) for all \(x\in R\) then \(a,b\in Z(R)\); when \(R\) is prime, \(1\in R\), \(\text{char\,}R\neq 2\), and \(xy^2x-yx^2y\in Z(R)\) for all \(x,y\in R\), then \(R\) is commutative.
Mathematics Subject Classification ID: 16W25
Mathematics Subject Classification ID: 16N60
Mathematics Subject Classification ID: 16U70
Mathematics Subject Classification ID: 16U80
zbMATH DE Number: 5077533
zbMATH Keywords: semiprime rings
zbMATH Keywords: commuting maps
zbMATH Keywords: generalized inner derivations
zbMATH Keywords: commutativity theorems
reviewed by: Charles Lanski
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5077533