Left annihilator of generalized derivations on Lie ideals in prime rings.
type: Item
instance of: scholarly article
title: Left annihilator of generalized derivations on Lie ideals in prime rings.
zbMATH Open document ID: 1328.16021
author: Faiza Shujat
author: Shahoor Khan
publication date: 2015-08-05T00:00:00Z
review text: For an associative ring \(R\), if \(d\in\text{der}(R)\) and \(F\colon R\to R\) is additive, so that for all \(x,y \in R\) \(F(xy)=F(x)y+xd(y)\) then \((F,d)\) is called a generalized derivation of \(R\). The authors assume that \(R\) is a prime ring, \(a\in R\), \(L\) is a noncentral Lie ideal of \(R\), and \((F,d)\) is a generalized derivation of \(R\). The main result of the paper assumes that \(n,k>0\), \(m_1,\ldots,m_k\geq 0\) are fixed integers, with some \(m_j>0\) and proves that if \(a(d(x)^{m_1}F(x)^{m_2}d(x)^{m_3}F(x)^{m_4}\cdots)^n\) is an identity for \(L\), then \(a=0\) or \(R\) embeds in \(M_2(C)\) for a field \(C\).
Mathematics Subject Classification ID: 16W25
Mathematics Subject Classification ID: 16N60
Mathematics Subject Classification ID: 16W10
Mathematics Subject Classification ID: 16R50
zbMATH DE Number: 6470001
zbMATH Keywords: generalized derivations
zbMATH Keywords: prime rings
zbMATH Keywords: Lie ideals
zbMATH Keywords: differential identities
reviewed by: Charles Lanski
MaRDI profile type: Publication
full work available at URL: s12215-014-0182-6
OpenAlex ID: W1982361201
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DOI: 10.1007/S12215-014-0182-6
published in: Rendiconti del Circolo Matematico di Palermo
description: scientific article