On generalized ∗-reverse derivable maps

Abstract

Let R be a ring with involution containing a nontrivial symmetric idempotent element e and δ: R → R be a generalized ∗-reverse derivable map. In this paper, our aim is to show that under some suitable restrictions imposed on R every generalized ∗-reverse derivable map of R is additive.

Multiplicative Generalized Reverse ∗ CE-Derivations Acting on Rings with Involution

“…Martindale [4] has asked the following question: When is a multiplicative mapping additive? He answered his question for a multiplicative isomorphism of a ring S. In [5], Daif has given an answer to that question when the mapping is a multiplicative derivation on S. Also, in [6][7][8], a generalization of this question can be found for the case of multiplicative generalized derivations, multiplicative generalized reverse * − derivations, and multiplicative left centralizers.…”