On the skew Lie product and derivations of prime rings with involution

Abstract

Let R be a ring with involution ′∗′. The skew Lie product of a, b ∈ R is defined by ∗[a, b] = ab − ba∗. The purpose of this paper is to study the commutativity of a prime ring which satisfies the various ∗-differential identities involving skew Lie product. Finally, we provide two examples to prove that the assumed restrictions on some of our results are not superfluous.