Comutativity Results on Semiprime Rings

Abstract

The purpose of this paper is to prove the following result:- Let R be a 2-torsion free semiprime ring. Z(R) be the center of R U be a nonzero ideal of R. and d be a nonzero derivation on R, then R contains a nonzero central ideal if one of the following conditions holds:   d"[x,y][xy] Z(R) for all x, y e U, where n is a fixed positive integer   d[xy]d[xy][x,y]eZ(R) for all x, y ∈ U. where p. m are fixed positive integers.