Identities with additive mappings in semiprime rings
Bull. Korean Math. Soc. 2014 Vol. 51, No. 1, 207-211
https://doi.org/10.4134/BKMS.2014.51.1.207
Printed January 1, 2014
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
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