Semigroup ideal in prime near-rings with derivations

الملخص EN

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 has 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.