An Engel condition with an additive mapping in semiprime rings.
type: Item
instance of: scholarly article
title: An Engel condition with an additive mapping in semiprime rings.
zbMATH Open document ID: 1317.16015
author: Maja Fošner
author: Nadeem-ur-Rehman
author: Joso Vukman
published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences
publication date: 2015-03-25T00:00:00Z
full work available at URL: https://dk.um.si/Dokument.php
review text: The aim of this article is to prove the following result: Let \(n>1\) be a fixed integer, let \(R\) be an \(n!\)-torsion free semiprime ring, and let \(f\colon R\to R\) be an additive mapping satisfying the relation \([f(x),x]_n=[[\cdots[[f(x),x],x],\cdots],x]=0\) for all \(x\in R\). Then \(f\) is a commuting map of \(R\), that is, \([f(x),x]=0\) for all \(x\in R\). Since von Neumann algebras and \(C^*\) algebras are always semiprime, this purely algebraic result might be of some interest from functional analysis point of view.
reviewed by: Feng Wei
Mathematics Subject Classification ID: 16N60
Mathematics Subject Classification ID: 16W25
Mathematics Subject Classification ID: 16W20
Mathematics Subject Classification ID: 16R50
Mathematics Subject Classification ID: 47B47
zbMATH DE Number: 6419539
zbMATH Keywords: semiprime rings
zbMATH Keywords: additive maps
zbMATH Keywords: derivations
zbMATH Keywords: Engel conditions
zbMATH Keywords: prime rings
zbMATH Keywords: commuting maps
zbMATH Keywords: centralizing maps
zbMATH Keywords: functional identities
MaRDI profile type: Publication
OpenAlex ID: W2072309139
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DOI: 10.1007/S12044-014-0205-4
description: scientific article; zbMATH DE number 6419539