Monatshefte für Mathematik

, Volume 95, Issue 4, pp 265–268 | Cite as

Near rings without zero divisors

  • Shalom Feigelstock
Article
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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

  1. [1]
    Ganesan, N.: Properties of rings with a finite number of zero divisors. Math. Ann.157, 215–218 (1964).Google Scholar
  2. [2]
    Graves, J.A., Malone, J.J.: Embedding near domains. Bull. Austral. Math. Soc.9, 33–42 (1973).Google Scholar
  3. [3]
    Heatherly, H., Olivier, H.: Near integral domains. Mh. Math.78, 215–222 (1974).Google Scholar
  4. [4]
    Heatherly, H., Olivier, H.: Near integral domains II. Mh. Math.80, 85–92 (1975).Google Scholar
  5. [5]
    Ligh, S.: On the additive groups of finite near integral domains and simple d. g. near rings. Mh. Math.76, 317–322 (1972).Google Scholar
  6. [6]
    Ligh, S., Malone, J.J.: Zero divisors and finite near rings. J. Austral. Math. Soc.11, 374–378 (1970).Google Scholar
  7. [7]
    Malone, J.J.: Near rings with trivial multiplications. Amer. Math. Soc. Monthly74, 1111–1112 (1967).Google Scholar
  8. [8]
    Pilz, G.: Near Rings. Amsterdam-New York-Oxford: North Holland. 1977.Google Scholar

Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • Shalom Feigelstock
    • 1
  1. 1.Bar-Ilan UniversityRamat GanIsrael

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