Jordan elementary maps on rings.
type: Item
instance of: scholarly article
title: Jordan elementary maps on rings.
zbMATH Open document ID: 1058.16022
author: Wu Jing
author: Pengtong Li
published in: Linear Algebra and its Applications
publication date: 2004-08-06T00:00:00Z
review text: There are many results in the literature showing that maps on rings that satisfy certain multiplicative conditions are necessarily additive. The paper continues this line of investigation. Specifically, the main result states that if \(R\) is a prime ring such that \(\text{char}(R)\neq 2\) and \(R\) contains a nontrivial idempotent, then surjective maps \(M\colon R\to R'\) and \(M^*\colon R'\to R\), where \(R'\) is an arbitrary ring, must be additive in case they satisfy the conditions \(M(xM^*(y)x)=M(x)yM(x)\) and \(M^*(yM(x)y)=M^*(y)xM^*(y)\) for all \(x\in R\), \(y\in R'\). These conditions appear in the definition of a Jordan elementary operator in the paper [Acta Sci. Math. 66, No. 3-4, 769-791 (2000; Zbl 0973.47028)] by \textit{M. Brešar}, \textit{L. Molnár} and \textit{P. Šemrl}.
Mathematics Subject Classification ID: 16N60
Mathematics Subject Classification ID: 47B47
Mathematics Subject Classification ID: 16W20
zbMATH DE Number: 2081913
zbMATH Keywords: Jordan elementary maps
zbMATH Keywords: prime rings
zbMATH Keywords: idempotents
zbMATH Keywords: additivity
zbMATH Keywords: additive maps
reviewed by: Matej Brešar
MaRDI profile type: Publication
full work available at URL: j.laa.2003.12.037
OpenAlex ID: W2026101053
cites work: Jordan mappings of semiprime rings
cites work: Elementary operators
cites work: Q2714340
cites work: Additivity of Elementary Maps on Rings
cites work: Jordan triple maps.
cites work: When are Multiplicative Mappings Additive?
cites work: On isomorphisms of standard operator algebras
cites work: Elementary Operators on Standard Operator Algebras
DOI: 10.1016/J.LAA.2003.12.037
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description: scientific article; zbMATH DE number 2081913