Semiprime Rings with Multiplicative Generalized Derivations on Lie Ideals

Abstract

Let be a torsion free semiprime ring. In [10], a map is called a multiplicative generalized derivation if there exists a map such that for all . Let be a noncentral square-closed Lie ideal of and multiplicative generalized derivations associated to the maps of respectively such that and for all In the present paper, we shall prove that is commuting map on if any one of the following holds: i) ii) If any one of the conditions iii) and iv) for all are satisfied,