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Affine planes, ternary rings, and examples of non-Desarguesian planes

The paper is devoted to a detailed self-contained exposition of a part of the theory of affine planes leading to a construction of affine (or, equivalently, projective) planes not satisfying the Desarques axiom. It is intended to complement the introductory expositions of the theory of affine and projective planes. A novelty of our exposition is a new notation for the ternary operation in a ternary ring, much more suggestive than the standard one.

preprint2016arXivOpen access
Nikolai V. Ivanov
math.CO
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Nikolai V. Ivanov

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