Additivity of Reverse Derivable Maps

Abstract

Let R be any ring containing a non-tivial idempotent element e. Let ℑ : R → R be a mapping such that ℑ(ab) = ℑ(b)a + bℑ(a) for all a, b ∈ R. In this note, our aim is to show that under some suitable restrictions imposed on R, ℑ is additive.