Additivity of $n$-Multiplicative Mappings of Gamma Rings

TL;DR

This paper proves that under certain conditions, n-multiplicative isomorphisms of Gamma rings are additive, extending understanding of their structure and behavior.

Contribution

It establishes the additivity of n-multiplicative isomorphisms and derivations on Gamma rings under specific conditions, a novel result in ring theory.

Findings

n-multiplicative isomorphisms are additive under certain conditions

Additivity of n-multiplicative derivations proved for Gamma rings

Extends the structural understanding of Gamma rings

Abstract

In this paper, we address the additivity of $n$-multiplicative isomorphisms and $n$-multiplicative derivations on Gamma rings. We proved that, if $\M$ is a $\Gamma$-ring satisfying the some conditions, then any $n$-multiplicative isomorphism $\left(\varphi, \phi\right)$ of $\M$ onto an arbitrary gamma ring is additive.