Vol. 96, No. 1, 1981

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Polynomial near-fields?

Yong Sian So

Vol. 96 (1981), No. 1, 213–223
Abstract

It is well known that all finite fields can be obtained as homomorphic images of polynomial rings. Hence it is natural to raise the question, which near-fields arise as homomorphic images of polynomial near-rings.

It is the purpose of this paper to give the surprising answer: one gets no proper near-fields at all—in dramatic contrast to ring and field theory. Another surprising result is the fact that all near-fields contained in the near-rings of polynomials are actually fields.

Mathematical Subject Classification 2000
Primary: 12K05
Milestones
Received: 15 December 1979
Published: 1 September 1981
Authors
Yong Sian So