Comutativity results on semiprime rings

الملخص EN

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'yX) >’]+ [.*,.)'] 6 Z(R) for all x, y gU , where n is a fixed positive integer.

ii- dp[x,y\+ dm\x,y\+ [jt,>>] e Z(R) for all x,ye U.

where p.

m are fixed positive integers.