Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2014; 51(1): 207-211

Printed January 1, 2014

https://doi.org/10.4134/BKMS.2014.51.1.207

Copyright © The Korean Mathematical Society.

Identities with additive mappings in semiprime rings

Ajda Fo\v sner and Nadeem ur Rehman

University of Primorska, Aligarh Muslim University

Abstract

The aim of this paper is to prove the next result. Let $n>1$ be an integer and let $R$ be a $n!$-torsion free semiprime ring. Suppose that $f:R\rightarrow R$ is an additive mapping satisfying the relation $[f(x),x^{n}]=0$ for all $x\in R$. Then $f$ is commuting on $R$.

Keywords: prime ring, semiprime ring, additive mapping, centralizing mapping, commuting mapping

MSC numbers: 16N60, 16R50