Multiplicative (generalized)-derivations of prime rings that act as $n-$(anti)homomorphisms

Abstract

Let $R$ be a prime ring. In this note, we describe the possible forms of multiplicative (generalized)-derivations of $R$ that act as $n-$homomorphism or $n-$antihomomorphism on nonzero ideals of $R.$ Consequently, from the given results one can easily deduce the results of Gusi\'{c} \cite{Gusic2005}.