Vanishing and cocentralizing generalized derivations on Lie ideals

ABSTRACTLet R be a prime ring of characteristic different from 2, U its right Utumi quotient ring, C its extended centroid and L a not central Lie ideal of R. Suppose that F, G and H are generalized derivations of R, with F≠0, such that F(G(x)x−xH(x)) = 0, for any x∈L. In this paper we describe all possible forms of F, G and H.