Lie ideals and generalized (α, β)-derivations of *-prime rings

Abstract

Let (R, *) be a 2-torsion free *-prime ring with involution *, L ≠ 0 be a square closed *-Lie ideal of R and α, β automorphisms of R commuting with *. An additive mapping F: R → R is called a generalized (α, β)-derivation on R if there exists an (α, β)-derivation d such that F(xy) = F(x)α(y) + β(x)d(y) holds for all \({x, y \in R}\). In the present paper, we shall show that \({L\subseteq Z(R)}\) such that R is a *-prime ring admits a generalized (α, β)-derivation satisfying several conditions, but associated with an (α, β)-derivation commuting with *.