Multiplicative (generalized)-derivation in semiprime rings

Abstract

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