Additivity of Reverse Derivable Maps

Abstract

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

There is a technical error in the hypothesis of the main result