{
  "id": "1905.09256",
  "version": "v1",
  "published": "2019-05-22T17:32:38.000Z",
  "updated": "2019-05-22T17:32:38.000Z",
  "title": "$F$-inverse monoids as algebraic structures in enriched signature",
  "authors": [
    "K. Auinger",
    "G. Kudryavtseva",
    "M. B. Szendrei"
  ],
  "comment": "21 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "Every $F$-inverse monoid can be equipped with the unary operation which maps each element to the maximum element of its $\\sigma$-class. In this enriched signature, the class of all $F$-inverse monoids forms a variety of algebraic structures. We describe universal objects in several classes of $F$-inverse monoids, in particular free $F$-inverse monoids. More precisely, for every $X$-generated group $G$ we describe the initial object in the category of all $X$-generated $F$-inverse monoids $F$ for which $F/\\sigma=G$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-22T17:32:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20M18",
      "20M07",
      "20M10"
    ],
    "keywords": [
      "algebraic structures",
      "enriched signature",
      "inverse monoids forms",
      "initial object",
      "universal objects"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}