Jordan higher centralizers on semiprime rings and related mappings.
type: Item
instance of: scholarly article
zbMATH Open document ID: 1308.16030
DOI: 10.5831/HMJ.2014.36.3.505
author: Yong-Soo Jung
published in: Honam Mathematical Journal
publication date: 2014-10-29T00:00:00Z
Mathematics Subject Classification ID: 16W25
Mathematics Subject Classification ID: 16N60
zbMATH DE Number: 6362201
zbMATH Keywords: Jordan higher derivations
zbMATH Keywords: Jordan higher left centralizers
zbMATH Keywords: semiprime rings
zbMATH Keywords: additive maps
MaRDI profile type: Publication
title: Jordan higher centralizers on semiprime rings and related mappings.
review text: Let \(R\) be a 2-torsion free semiprime ring with \(J=(\delta_i)_{i\geq 0}\) and \(I=(\varphi_i)_{i\geq 0}\) two sequences of additive maps \(\delta_i,\varphi_j\colon R\to R\) with \(\delta_0=id_R\) and \(\varphi_0=0\). Call \(J\) a Jordan higher derivation of \(R\) if for all \(a\in R\), \(\delta_n(a^2)=\sum_{n=i+j}\delta_i(a)\delta_j(a)\), call \(I\) a higher left centralizer for \(J\) if for all \(a,b\in R\), \(\varphi_n(ab)=\sum_{n=i+j}\varphi_i(a)\delta_j(b)\), and call \(I\) a Jordan higher left centralizer for \(J\) if for all \(a\in R\), \(\varphi_n(a^2)=\sum_{n=i+j}\varphi_i(a)\delta_j(a)\).NEWLINENEWLINE The main result in the paper shows that if \(I\) is a Jordan higher left centralizer for \(J\), then \(I\) is a higher left centralizer for \(J\).
reviewed by: Charles Lanski
description: scientific article; zbMATH DE number 6362201