Daif and SCP – Derivations on Semigroup Ideal I of a Near–ring N

Abstract

Abstract.In this paper we study two kinds of derivations on a semigroup ideal I of a near ring N. The first kind called Daif derivation (Daif 1 derivation and Daif 2 derivation), the second kind is called strong commutativity preserving derivations. Bell and Mason, showed that a prime near ring N must be commutative if it admits any of these kinds of derivations, and we generalize this to a semigroup ideal I.