Derivations satisfying certain algebraic identities on Jordan ideals.
type: Item
instance of: scholarly article
title: Derivations satisfying certain algebraic identities on Jordan ideals.
zbMATH Open document ID: 1273.16038
published in: Arabian Journal of Mathematics
publication date: 2012-12-06T00:00:00Z
review text: A ring \(R\) with involution * is defined to be *-prime if \(aRb=aRb^*=\{0\}\) implies \(a=0\) or \(b=0\). An additive subgroup \(J\) is called a *-Jordan ideal if \(J^*=J\) and \(xr+rx\in J\) for all \(x\in J\) and \(r\in R\). It is proved that if a 2-torsion free *-prime ring with nonzero *-Jordan ideal \(J\) admits a nonzero derivation \(d\) such that \(d([x,y])=0\) for all \(x,y\in J\) or \(d([x,y])=[x,y]\) for all \(x,y\in J\), then \(R\) is commutative.
Mathematics Subject Classification ID: 16W10
Mathematics Subject Classification ID: 16W25
Mathematics Subject Classification ID: 16U70
Mathematics Subject Classification ID: 16U80
Mathematics Subject Classification ID: 16N60
zbMATH DE Number: 6112840
zbMATH Keywords: rings with involution
zbMATH Keywords: *-prime rings
zbMATH Keywords: *-Jordan ideals
zbMATH Keywords: derivations
zbMATH Keywords: commutativity theorems
Wikidata QID: Q59288418
author: Lahcen Oukhtite
author: Abdellah Mamouni
MaRDI profile type: Publication
full work available at URL: s40065-012-0039-9
OpenAlex ID: W2064722134
cites work: Lie and Jordan Structure in Prime Rings with Derivations
cites work: On derivations and commutativity in prime rings
cites work: Remarks on derivations on semiprime rings
cites work: Posner's second theorem for Jordan ideals in rings with involution.
cites work: Q3083870
cites work: On derivations in \sigma-prime rings
cites work: On commutativity of sigma-prime rings
cites work: Generalized derivations centralizing on Jordanideals of rings with involution
cites work: On Jordan ideals and left \((\theta,\theta)\)-derivations in prime rings.
DOI: 10.1007/S40065-012-0039-9
description: scientific article; zbMATH DE number 6112840