Polynomial near-fields?

Yong Sian So

Vol. 96 (1981), No. 1, 213–223

DOI: 10.2140/pjm.1981.96.213

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