Identities with generalized derivations in prime rings.
type: Item
instance of: scholarly article
title: Identities with generalized derivations in prime rings.
zbMATH Open document ID: 1262.16043
author: Maja Fošner
author: Joso Vukman
published in: Mediterranean Journal of Mathematics
publication date: 2012-11-23T00:00:00Z
review text: Let \(R\) be a prime ring with \(\text{char\,}R\neq 2\), \(Q_l\) and \(Q_r\) the left and right Martindale quotient rings of \(R\), and \(F,G\colon R\to R\) generalized derivations of \(R\). The authors prove that if for all \(x\in R\), \(F(x)G(x)=0\) then \(F(x)=xa\) for \(a\in Q_l\) and \(G(x)=bx\) for \(b\in Q_r\) with \(ab=0\). When \(F(x)G(x)+G(x)F(x)=0\) for all \(x\in R\) then either \(F=0\) or \(G=0\).
reviewed by: Charles Lanski
Mathematics Subject Classification ID: 16W25
Mathematics Subject Classification ID: 16N60
Mathematics Subject Classification ID: 16R60
zbMATH DE Number: 6110335
zbMATH Keywords: prime rings
zbMATH Keywords: generalized derivations
zbMATH Keywords: functional identities
MaRDI profile type: Publication
full work available at URL: s00009-011-0158-0
OpenAlex ID: W2081283626
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DOI: 10.1007/S00009-011-0158-0
description: scientific article; zbMATH DE number 6110335