On $\ast -$Reverse Derivable Maps

Abstract

Let $R$ be a ring with involution containing a nontrivial symmetric idempotent element $e$. Let $\hat{I}´:R\to R$ be a mapping such that $\hat{I}´(ab)=\hat{I}´(b)a^{\ast }+b^{\ast }\hat{I}´(a)$ for all $a,b\in R$, we call $\hat{I}´$ a $\ast -$reverse derivable map on $R$. In this paper, our aim is to show that under some suitable restrictions imposed on $R$, every $\ast -$reverse derivable map of $R$ is additive.