Multiplicative (generalized)-derivation in semiprime rings

摘要

Let R be a semiprime ring and α anymapping on R.Amapping 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 ofmappings.