Some Commutativity Theorems in Prime Rings with Involution and Derivations

Let R be a ring with involution ′∗′ . An additive map x → x* of R into itself is called an involution if (i) (xy)*= y∗x∗ and (ii) (x∗)∗ = x holds for all x,y ∈ R. An additive mapping δ: R → R is called a derivation if δ(xy) = δ(x)y + xδ(y) for all x, y ∈ R. The purpose of this paper is to examine the commutativity of prime rings with involution satisfying certain identities involving derivations.