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The concept of $\Gamma$-ring is a generalization of ring. Twoimportant classes of $\Gamma$-rings are prime and semi-prime$\Gamma$-rings. In this paper, we consider the concept of derivations on prime and semi-prime $\Gamma$-rings and we study some of their properties.

Let R be a 2-torsion free sigma-prime ring with an involution sigma, I a nonzero sigma-ideal of R. In this paper we explore the commutativity of R satisfying any one of the properties: (i) d(x) oF(y) = 0 for all x, y ∈ I. (ii) [d(x), F(y)] = 0 for all x, y ∈ I. (iii) d(x) o F(y) = x o y for all x, y ∈ I. (iv) d(x)F(y) − xy ∈ Z(R) for all x, y ∈ I. We also discuss (alpha ,beta )-derivations of sigma-prime rings and prove that if G is an (alpha ,beta)-derivation which acts as a homomorphism or as an anti-homomorphism on I, then G = 0 or G = beta on I.