On nilpotent homoderivations in semi-prime rings

Abstract

Let $R$ be an associative ring and let $s \geq 1$ be a fixed integer. An additive map $h$ on $R$ is called a homoderivation if $h(xy) = h(x)h(y) + h(x)y + xh(y)$ holds for all $x, y \in R.$ In \cite{Chung83,Chung84,Luh84}, Chung and Luh proved several results about the nilpotency of derivations in semi-prime rings. Similarly, the main objective of this paper is to provide a complete study about the nilpotency of homoderivations with nilpotency `$s$' in semi-prime rings.