Some results in semiprime rings with derivation

Abstract

Let R be a semiprime ring and S be a nonempty subset of R: A mapping F from R to R is called centralizing on S if [F(x); x] 2 Z for all x 2 S. The mapping F is called strong commutativity preserving (SCP) on S if [F(x); F(y)] = [x; y] for all x; y 2 S: In the present paper, we investigate some relationships between centralizing derivations and SCP-derivations of semiprime rings. Also, we study centralizing properties derivation which acts homomorphism or anti-homomorphism in semiprime rin