Notes on Generalized $(\sigma ,\tau )$-Derivation

Abstract

Let R be a prime ring with char R ≠ 2 and let σ, τ be automorphisms of R. An additive mapping f : R → R is called a generalized (σ, τ)–derivation if there exists a (σ, τ)–derivation d : R → R such that f(xy) = f(x)σ(y)+τ_(x)d(y)_ holds for all x,y ∈ R. In this paper some well known results concerninggeneralized derivations of prime rings are extended to generalized (σ, τ)–derivations.