Abstract
Let R be a 2-torsion free ring and L a Lie ideal of R. An additive mapping F R -> R is called a generalized derivation on R if there exists a derivation d R -> R such that F(xy) = F(x)y+xd(y) holds for all x, y is an element of R. In the present paper we describe the action of generalized derivations satisfying several conditions on Lie ideals of semiprime rings.