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

Abstract

Let be a prime Γ-ring satisfying for all and with center Z, and U be a Lie (Jordan) ideal. A mapping is called Γ- centralizing if for all and .In this paper , we studied Lie and Jordan ideal in a prime Γ - ring M together with Γ -centralizing derivations on U.