Jordan derivations and Jordan homomorphisms on prime rings of characteristic 2
type: Item
instance of: scholarly article
title: Jordan derivations and Jordan homomorphisms on prime rings of characteristic 2
zbMATH Open document ID: 0639.16021
DOI: 10.1007/BF01903618
author: R. Awtar
published in: Acta Mathematica Hungarica
publication date: 1988-01-01T00:00:00Z
review text: The main result of this paper shows that if \(T\) is a bijective and additive mapping from a ring \(R\) to a noncommutative prime ring \(S\) of characteristic 2, and if \(T\) satisfies \(T(xy+yx)=T(x)T(y)+T(y)T(x)\) and \(T(x^3)=T(x)^3\) for all \(x,y\in R\), then \(T\) is either an isomorphism or an anti-isomorphism. This theorem extends a similar one of \textit{I. N. Herstein} and \textit{E. Kleinfeld} [Pac. J. Math. 10, 843-852 (1960; Zbl 0093.040)] by making some slight modifications in its proof. The earlier result assumes that \(T\) is onto and that \(R\) and \(S\) are simple rings. The author also asserts that when \(D\) is an additive mapping from the noncommutative prime ring \(R\) of characteristic 2 to itself so that \(D\) acts like a derivation on commutators and on cubes, then \(D\) is a derivation of \(R\). This extends a result of \textit{I. N. Herstein} [Proc. Am. Math. Soc. 8, 1104-1110 (1958; Zbl 0216.07202)] which assumes that \(D\) acts like a derivation on commutators and on products of the form \(xyx\).
reviewed by: Charles Lanski
Mathematics Subject Classification ID: 16W20
Mathematics Subject Classification ID: 16N60
Mathematics Subject Classification ID: 16W10
zbMATH DE Number: 4042112
zbMATH Keywords: Jordan derivations
zbMATH Keywords: Jordan homomorphisms
zbMATH Keywords: additive mappings
zbMATH Keywords: prime rings
zbMATH Keywords: anti-isomorphisms
zbMATH Keywords: simple rings
zbMATH Keywords: commutators
zbMATH Keywords: cubes
MaRDI profile type: Publication
cites work: Lie mappings in characteristic 2
cites work: Jordan Derivations of Prime Rings
cites work: Jordan Homomorphisms Onto Prime Rings
full work available at URL: https://doi.org/10.1007/bf01903618
OpenAlex ID: W2024886308
description: scientific article; zbMATH DE number 4042112