Lie Ideals and Centralizing Mappings with Generalized Derivations

Abstract

Let R be a prime ring with char(R) ≠ 2, Z(R) the center of R and L be a nonzero square closed Lie ideal of R. An additive mapping F : R → R is called a generalized derivation on R if there exists a derivation d : R → Rsuch that F(xy) = xF(y) + d(x)y for all x, y ∈ R. In the present paper we shall show that L ⊆ Z(R) such that Radmitting a generalized derivations F and G associated with derivations d and g respectively, satisfying several conditions.