{
  "id": "2303.15797",
  "version": "v1",
  "published": "2023-03-28T08:02:17.000Z",
  "updated": "2023-03-28T08:02:17.000Z",
  "title": "Distributivity in congruence lattices of graph inverse semigroups",
  "authors": [
    "Yongle Luo",
    "Zhengpan Wang",
    "Jiaqun Wei"
  ],
  "comment": "11 pages, 3 figures",
  "categories": [
    "math.GR"
  ],
  "abstract": "Let {\\Gamma} be a directed graph and Inv({\\Gamma}) be the graph inverse semigroup of {\\Gamma}. Luo and Wang [7] showed that the congruence lattice C(Inv({\\Gamma})) of any graph inverse semigroup Inv({\\Gamma}) is upper semimodular, but not lower semimodular in general. Anagnostopoulou-Merkouri, Mesyan and Mitchell characterized the directed graph {\\Gamma} for which C(Inv({\\Gamma})) is lower semimodular [2]. In the present paper, we show that the lower semimodularity, modularity and distributivity in the congruence lattice C(Inv({\\Gamma})) of any graph inverse semigroup Inv({\\Gamma}) are equivalent.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-03-28T08:02:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20M18",
      "05C20",
      "06D99"
    ],
    "keywords": [
      "graph inverse semigroup",
      "congruence lattice",
      "distributivity",
      "directed graph",
      "upper semimodular"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}