Posner’s Theorems For Generalized M-Derivations

Abstract

In this article, we introduce an additive map G: R → R on ring R associated with multiplicative
derivation d on R such that G(xy) = G(x)y + xd(y) for all x, y ∈ R and termed it generalized mderivations. Our aim is to extend the remarkable results of Posner on derivations to generalized mderivations. The study of this mapping ensures the commutativity of prime rings which is viable
algebraic structure and favorable to study the other field of algebras and computational mathematics
such as C*-algebras, B*-algebras, functional analysis and automata theory.