Generalized derivations on Lie ideals in prime rings

Abstract

Let R be a prime ring with characteristic different from two, U a nonzero Lie ideal of R and f be a generalized derivation associated with d. We prove the following results: (i) If [u, f (u)] is an element of Z, for all u is an element of U, then U subset of Z. (ii) (f,d) and (g,h) be two generalized derivations of R such that f (u)v = ug(v), for all u,v is an element of U, then U subset of Z. (iii) f([u,v]) = +/-[u,v], for all u, v is an element of U, then U subset of Z.