{
  "id": "1601.01922",
  "version": "v1",
  "published": "2016-01-08T16:01:37.000Z",
  "updated": "2016-01-08T16:01:37.000Z",
  "title": "Algebras with Parastrophically Uncancellable Quasigroup Equations",
  "authors": [
    "Amir Ehsani",
    "Aleksandar Krapež",
    "Yuri Movsisyan"
  ],
  "comment": "23 pages, 2 figures, submitted to Buletinul Academiei de \\c{S}tiin\\c{t}e a Republicii Moldova. Matematica",
  "categories": [
    "math.GR"
  ],
  "abstract": "We consider $48$ parastrophically uncancellable quadratic functional equations with four object variables and two quasigroup operations in two classes: balanced non--Belousov (consists of 16 equations) and non--balanced non--gemini (consists of 32 equations). A linear representation of a group (Abelian group) for a pair of quasigroup operations satisfying one of these parastrophically uncancellable quadratic equations is obtained. As a consequence of these results, a linear representation for every operation of a binary algebra satisfying one of these hyperidentities is presented.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-08T16:01:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20N05",
      "39B52",
      "08A05"
    ],
    "keywords": [
      "parastrophically uncancellable quasigroup equations",
      "linear representation",
      "quasigroup operations",
      "parastrophically uncancellable quadratic functional equations",
      "parastrophically uncancellable quadratic equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160101922E"
    }
  }
}