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: i- d^n [x,y] ±4 [x,y] ϵ Z(R) for all x.y ϵ U.where n isa fixed positive integer. ii- d ^ p [x, y ]±4 d ^ m [x, y ]± [x, y ] ϵ Z(R) 1)for all x,y ϵ U. where p. m are fixed positive integers.
