{
  "id": "1604.04945",
  "version": "v1",
  "published": "2016-04-18T00:20:45.000Z",
  "updated": "2016-04-18T00:20:45.000Z",
  "title": "Affine planes, ternary rings, and examples of non-Desarguesian planes",
  "authors": [
    "Nikolai V. Ivanov"
  ],
  "comment": "25 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-04-18T00:20:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "51E15",
      "51A35",
      "12K99"
    ],
    "keywords": [
      "affine planes",
      "non-desarguesian planes",
      "ternary ring",
      "introductory expositions",
      "ternary operation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}