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.
Ajda Fo\v sner and Nadeem ur Rehman
University of Primorska, Aligarh Muslim University
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
2014; 51(4): 1127-1133
2013; 50(6): 1863-1871
2007; 44(4): 789-794
2021; 58(3): 659-668
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd