Generalized Derivations in Semiprime Gamma Rings

Abstract

Let M be a 2-torsion-free semiprime Γ-ring satisfying the condition aαbβc aβbαc for all a, b, c ∈ M, α, β ∈ Γ, and let D : M → M be an additive mapping such that D xαx D x αx xαd x for all x ∈ M, α ∈ Γ and for some derivation d of M. We prove that D is a generalized derivation.

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