Jordan \(\sigma\)-derivations of prime rings
type: Item
instance of: scholarly article
title: Jordan \(\sigma\)-derivations of prime rings
zbMATH Open document ID: 1371.16020
DOI: 10.1216/RMJ-2017-47-2-511
author: Tsiu-Kwen Lee
published in: Rocky Mountain Journal of Mathematics
publication date: 2017-05-16T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.rmjm/1492502548
review text: In this paper, a complete characterization is given for Jordan \(\sigma\)-derivations of a prime ring \(R\) with \(\sigma\) an epimorphism. Such a Jordan \(\sigma\)-derivation \(\delta:R\rightarrow Q_{mr}(R)\) is either a \(\sigma\)-derivation or \(\delta(x)=ud(x)+\mu(x)u\) for all \(x\in R\) for some derivation \(d:R\rightarrow Q_{mr}(R)\), unit \(u\in Q_{mr}(R)\), and additive map \(\mu:R\rightarrow C\) satisfying \(\mu(x^{2})=0\) for all \(x\in R\). In case that \(\sigma\) is an X-outer automorphism, \(\delta\) is always a \(\sigma\)-derivation. A major part of the proof is to handle the case where \(R\) is a prime GPI-ring but is not a PI-ring, and the tool is built using the theory of functional identities.
reviewed by: Wen-Fong Ke
Mathematics Subject Classification ID: 16N60
Mathematics Subject Classification ID: 16R60
Mathematics Subject Classification ID: 16W25
zbMATH DE Number: 6715759
zbMATH Keywords: prime ring
zbMATH Keywords: (Jordan) \(\sigma\)-derivation
zbMATH Keywords: PI
zbMATH Keywords: GPI
zbMATH Keywords: functional identity
MaRDI profile type: Publication
Wikidata QID: Q57787497
description: scientific article; zbMATH DE number 6715759