On Semiderivations in Prime Gamma Rings

Abstract

Let M be a prime gamma ring. Let d : M → M be a semiderivation associated with a function g : M → M. We prove that d must be an ordinary derivation or of the form d(x) = pδ(x − g(x)) for all x∈M, δ∈Γ, where p is an element of the extended centroid of M. We have also seen that g must necessarily be an endomorphism.