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

Abstract

Let $R$ be a prime ring with $\text{char}R\ne 2$ and let $\sigma ,\tau$ be automorphisms of $R$. An additive mapping $f:R\to R$ is called a generalized $(\sigma ,\tau )$-derivation if there exists a $(\sigma ,\tau )$-derivation $d:R\to R$ such that $f(xy)=f(x)\sigma (y{)}_{+}\tau (x)d(y)$ holds for all $x,y\in R$. In this paper some well known results concerning generalized derivations of prime rings are extended to generalized $(\sigma ,\tau )$-derivations.