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

TL;DR

This paper characterizes multiplicative (generalized)-derivations in prime rings that behave as n-homomorphisms or n-antihomomorphisms on nonzero ideals, extending previous results in ring theory.

Contribution

It provides a classification of such derivations in prime rings, offering a broader understanding of their structure and behavior.

Findings

Describes possible forms of multiplicative derivations acting as n-(anti)homomorphisms.

Extends and generalizes results of Gusic (2005).

Offers a framework for analyzing derivations in prime rings.

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}.