Let M be a semiprime Γ-ring with involution satisfying the condition that aαbβc = aβbαc (a, b, c ∈ M and α, β ∈ Γ). An additive mapping. In this paper we will prove that if d is Γ * -derivation of a semiprime Γ-ring with involution which is either an endomorphism or anti-endomorphism, then d=0.

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.

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