On a generalization of reverse derivation of certain algebraic structure

Abstract

In this paper, a generalization of gamma ring (symbolically, Г-ring) called generalized Г-ring is established. We define a generalization of reverse derivation, called a reverse f-derivation on generalized Г-ring M which is an additive mapping d : M ➝ M, satisfying d(xαy) = d(y)α f(x) + f(y)αd(x) and d(f(x)) = f(d(x)) for all x, y ∈ M and a ϵ G, where f is an automorphism of M. We obtain some conditions on M which force that the zero map is the only reverse f-derivation on M. Moreover, we investigate the commutativity of M satisfying some conditions involving reverse f-derivations.