Notes on prime near-rings with multiplicative derivation

TL;DR

This paper investigates the properties of prime near-rings with nonzero multiplicative derivations, extending known results about commutativity in prime rings to the near-ring context.

Contribution

It extends classical results on ring commutativity to prime near-rings with multiplicative derivations, providing new insights into their structure.

Findings

Prime near-rings with nonzero multiplicative derivations exhibit conditions leading to commutativity.

Extension of classical ring results to near-ring structures.

New criteria for commutativity in prime near-rings with derivations.

Abstract

Let N be a left near ring. A map d on N is called a nonzero multiplicative derivation if d(xy)=xd(y)+d(x)y holds for all x,y elements of N.In the present paper, we shall extend some well known results concerning commutativity of prime rings for a nonzero multiplicative derivations of a left prime near-ring N.