{
  "id": "1810.02405",
  "version": "v1",
  "published": "2018-10-04T19:55:30.000Z",
  "updated": "2018-10-04T19:55:30.000Z",
  "title": "Residuation in non-associative MV-algebras",
  "authors": [
    "Ivan Chajda",
    "Helmut Länger"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "It is well known that every MV-algebra can be converted into a residuated lattice satisfying divisibility and the double negation law. In our previous papers we introduced the concept of an NMV-algebra which is a non-associative modification of an MV-algebra. The natural question arises if an NMV-algebra can be converted into a residuated structure, too. Contrary to MV-algebras, NMV-algebras are not based on lattices but only on directed posets and the binary operation need not be associative and hence we cannot expect to obtain a residuated lattice but only an essentially weaker structure called a conditionally residuated poset. Considering several additional natural conditions we show that every NMV-algebra can be converted in such a structure. Also conversely, every such structure can be organized into an NMV-algebra. Further, we study a bit more stronger version of an algebra where the binary operation is even monotonous. We show that such an algebra can be organized into a residuated poset and, conversely, every residuated poset can be converted in this structure.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-04T19:55:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "06D35",
      "03G10",
      "06A11"
    ],
    "keywords": [
      "non-associative mv-algebras",
      "nmv-algebra",
      "residuated poset",
      "binary operation",
      "residuation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}