{
  "id": "1306.3335",
  "version": "v1",
  "published": "2013-06-14T08:43:02.000Z",
  "updated": "2013-06-14T08:43:02.000Z",
  "title": "MV-algebras freely generated by finite Kleene algebras",
  "authors": [
    "Stefano Aguzzoli",
    "Leonardo M. Cabrer",
    "Vincenzo Marra"
  ],
  "comment": "27 pages, 8 figures. Submitted to Algebra Universalis",
  "journal": "Algebra universalis, November 2013, Volume 70, Issue 3, pp 245-270",
  "doi": "10.1007/s00012-013-0250-3",
  "categories": [
    "math.LO",
    "math.CT",
    "math.GT"
  ],
  "abstract": "If V and W are varieties of algebras such that any V-algebra A has a reduct U(A) in W, there is a forgetful functor U: V->W that acts by A |-> U(A) on objects, and identically on homomorphisms. This functor U always has a left adjoint F: W->V by general considerations. One calls F(B) the V-algebra freely generated by the W-algebra B. Two problems arise naturally in this broad setting. The description problem is to describe the structure of the V-algebra F(B) as explicitly as possible in terms of the structure of the W-algebra B. The recognition problem is to find conditions on the structure of a given V-algebra A that are necessary and sufficient for the existence of a W-algebra B such that F(B) is isomorphic to A. Building on and extending previous work on MV-algebras freely generated by finite distributive lattices, in this paper we provide solutions to the description and recognition problems in case V is the variety of MV-algebras, W is the variety of Kleene algebras, and B is finitely generated--equivalently, finite. The proofs rely heavily on the Davey-Werner natural duality for Kleene algebras, on the representation of finitely presented MV-algebras by compact rational polyhedra, and on the theory of bases of MV-algebras.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-06-14T08:43:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "06D35",
      "06D30",
      "06D50",
      "03C05"
    ],
    "keywords": [
      "finite kleene algebras",
      "mv-algebras",
      "recognition problem",
      "compact rational polyhedra",
      "davey-werner natural duality"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1306.3335A"
    }
  }
}