Abstract
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 domainN 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 ofGanesan [1] on the non-zero divisors in a finite ring is generalized to near rings.
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References
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Feigelstock, S. Near rings without zero divisors. Monatshefte für Mathematik 95, 265–268 (1983). https://doi.org/10.1007/BF01547797
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DOI: https://doi.org/10.1007/BF01547797