Generalized higher derivations on algebras

Abstract

We study the structure of generalized higher derivations on an algebra ${\scr A}$ and show that there exists a one-to-one correspondence between the set of all generalized higher derivations $\{ G_k\}^n_{k =0}$ on ${\scr A}$ with $G_0 = I$ and the set of all sequences $\{ g_k\}^n_{k = 0}$ of generalized derivations on ${\scr A}$ with $g_0 = 0$.