In the present paper, we prove that 3–prime near-ring N is commutative ring, if any one of the following conditions are satisfied: (i) f (N) ⊆ Z, (ii) f ([x, y]) = 0, (iii) f ([x, y]) = ±τ ([x, y]), (iv) f ([x, y]) = ±τ(xoy), (v) f ([x, y]) = τ ([d(x), y]), for all x, y ∈ N, where f is a nonzero left multiplicative generalized (σ, τ)-derivation of N associated with a multiplicative (σ, τ)-derivation d.
Topics
Ring theory
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