Let U be an Γ-ring and M be an irreducible UΓ-moduie, for α∈U, α∈Γ, we define T[a,a]: M→M by m T[a,a] = maa for all m∈M. Let End(M) be the ring of all endomorphisms of the additive group of M. We define as usual End[Γ,U](M)=={ψ∈End(M)|TΣ[ai,ai]ψ=ψTΣ[ai,ai] all ai∈U,ai∈Γ}. In this paper the following results are obtained. |