Lie and Jordan Structure in Prime Γ- rings with Γ-centralizing Derivations

Let M be a prime Γ-ring satisfying aab Bc=aBbac for all a,b,c element of M and a,B element Γ with center Z, and U be a Lie (Jordan) ideal. A mapping d :M rightarrow M is called Γ- centralizing if [u, d (u)] a element of Z for all u element of U and a element of Γ .In this paper , we studied Lie and Jordan ideal in a prime Γ - ring M together with Γ - centralizing derivations on U.