Abstract :
Let R be a ∗-prime ring with center Z(R), d a non-zero (σ,τ)-derivation of R with associated automorphisms σ and τ of R, such that σ, τ and d commute with ′∗′. Suppose that U is an ideal of R such that U∗=U, and Cσ,τ={c∈R | cσ(x)=τ(x)c for~all x∈R}. In the present paper, it is shown that if characteristic of R is different from two and [d(U),d(U)]σ,τ={0}, then R is commutative. Commutativity of R has also been established in case if [d(R),d(R)]σ,τ⊆Cσ,τ.
