Multiplicative (generalized)-derivation in semiprime rings

Abstract

Let R be a semiprime ring and α any mapping on R. A mapping F: R→ R is called multiplicative (generalized)-derivation if F(xy) = F(x) y+ xd(y) for all x, y∈ R, where d: R→ R is any map (not necessarily additive). In this paper our main motive is to study the commutativity of semiprime rings and nature of mappings.