Some properties of prime near-rings with (σ, τ)-derivation

Some results by Bell and Mason on commutativity in near-rings are generalized. Let N be a prime right near-ring with multiplicative center Z and let D be a (sigma, tau)-derivation on N such that sigma D = D sigma and tau D = D tau. The following results are proved: (i) If D(N) subset of Z or [D(N), D(N)] = 0 or [D(N),D(N)](sigma,tau) = 0 then (N,+) is abelian; (ii) If D(xy) = D(x)D(y) or D(xy) = D(y)D(x) for all x,y is an element of N then D = 0.