{
  "id": "2008.10539",
  "version": "v1",
  "published": "2020-08-24T16:22:44.000Z",
  "updated": "2020-08-24T16:22:44.000Z",
  "title": "Relationships among quasivarieties induced by the min networks on inverse semigroups",
  "authors": [
    "Ying-Ying Feng",
    "Li-Min Wang",
    "Zhi-Yong Zhou"
  ],
  "doi": "10.1007/s00233-020-10126-1",
  "categories": [
    "math.GR"
  ],
  "abstract": "A congruence on an inverse semigroup $S$ is determined uniquely by its kernel and trace. Denoting by $\\rho_k$ and $\\rho_t$ the least congruence on $S$ having the same kernel and the same trace as $\\rho$, respectively, and denoting by $\\omega$ the universal congruence on $S$, we consider the sequence $\\omega$, $\\omega_k$, $\\omega_t$, $(\\omega_k)_t$, $(\\omega_t)_k$, $((\\omega_k)_t)_k$, $((\\omega_t)_k)_t$, $\\cdots$. The quotients $\\{S/\\omega_k\\}$, $\\{S/\\omega_t\\}$, $\\{S/(\\omega_k)_t\\}$, $\\{S/(\\omega_t)_k\\}$, $\\{S/((\\omega_k)_t)_k\\}$, $\\{S/((\\omega_t)_k)_t\\}$, $\\cdots$, as $S$ runs over all inverse semigroups, form quasivarieties. This article explores the relationships among these quasivarieties.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-24T16:22:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20M18"
    ],
    "keywords": [
      "inverse semigroup",
      "min networks",
      "relationships",
      "form quasivarieties"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}