{
  "id": "1402.5136",
  "version": "v5",
  "published": "2014-02-18T17:31:54.000Z",
  "updated": "2015-02-10T22:23:19.000Z",
  "title": "Finitely based monoids",
  "authors": [
    "Olga Sapir"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "We present a method for proving that a semigroup is finitely based and find some new sufficient conditions under which a monoid is finitely based. As an application, we find a class of finite monoids where the finite basis property behaves in a complicated way with respect to the lattice operations but can be recognized by a simple algorithm. The method results in a short proof of the theorem of E. Lee that every monoid that satisfies xtxysy = xtyxsy and xytxsy = yxtxsy is finitely based. Also, the method gives an alternative proof of the theorem of F. Blanchet-Sadri that a pseudovariety of n-testable languages is finitely based if and only if n < 4.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2014-03-07T13:07:32.000Z",
      "abstract": "We present a method for proving that a semigroup is finitely based and find some new sufficient conditions under which a monoid is finitely based. Our method also gives a short proof to the theorem of E. Lee that every monoid that satisfies xtxysy = xtyxsy and xytxsy = yxtxsy is finitely based.",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v5",
      "updated": "2015-02-10T22:23:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "sufficient conditions",
      "short proof",
      "satisfies xtxysy"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1402.5136S"
    }
  }
}