Near rings without zero divisors

Near rings without zero divisors, and a dual structure, near codomains, are studied. It is shown that a near ring is a near field if and only if it is an integral near ring, a near codomain, and has a non-zero distributive element. If the additive group (N, +) of a near integral domain N is cohopfian, then (N, +) possesses a fixed point free automorphism which is either torsion free or of prime order. This generalizes a well-known theorem of Ligh for finite near integral domains. A result of Ganesan [1] on the non-zero divisors in a finite ring is generalized to near rings.