A remark on centralizers in semiprime rings

Abstract

The purpose of this paper is to prove the following result: Let m 1, n 1 be xed integers and let R be a (m+n+2)!-torsion free semiprime ring with the identity element. Suppose there exists an additive mapping T : R ! R, such that T(x m+n+1 ) = x m T(x)x n holds for all x 2 R. In this case T is a centralizer.