Generalized k- Derivations on Lie Ideals of Prime Γ-Rings

Abstract

Abstract: Let M be a 2-torsion free prime Γring and U a Lie ideal of M. Let F : M → M be a mapping defined by F (uαv) = F(u)αv + uk(α)v + uαd(v), for all u ,v  U and α  Γ. Then F is a generalized kderivation on U of M if there exists a kderivation d on U of M. Also F is a Jordan generalized kderivation on U of M if there exists a k derivation d on U of M such that F(uαu) = F(u)αu + uk(α)u + uαd(u), for all u  U and α  Γ. In this article, we prove that every Jordan generalized k derivation on a Lie ideal U of a 2 torsion free prime Γring M is a generalized k derivation on U of M.