ABSTRACT. We obtain conditions on (R, +) which force that the zero map is the only derivation on a zero-symmetric near-ring R. Throughout the paper we construct several new examples of near-rings which are not rings admitting non-zero derivations, non-zero (σ, σ)-derivations and non-zero (1, σ)-derivations.

In this paper we study some conditions under which a near-ring R admitting a (multiplicative) (σ, τ )-derivation d must be a commutative ring with constrained-suitable conditions on d, σ and τ . Consequently, we obtain some results which generalize some recent theorems in the literature.

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