Semigroup ideal in Prime Near-Rings with Derivations

Abstract

In this paper we generalize some of the results due to Bell and Mason on a near-ring N admitting a derivation D , and we will show that the body of evidence on prime near-rings with derivations have the behavior of the ring. Our purpose in this work is to explore further this ring like behavior. Also, we show that under appropriate additional hypothesis a near-ring must be a commutative ring.

Keywords

• Prime Near-ring , Semiprime Near–ring, Semigroup ideal, derivation. Mathematical Subject Classification: 16Y30 , 16W25 , 15U80.