{
  "id": "1903.07100",
  "version": "v1",
  "published": "2019-03-17T14:42:07.000Z",
  "updated": "2019-03-17T14:42:07.000Z",
  "title": "A new approach to a network of congruences on an inverse semigroup",
  "authors": [
    "Ying-Ying Feng",
    "Li-Min Wang",
    "Lu Zhang",
    "Hai-Yuan Huang"
  ],
  "doi": "10.1007/s00233-019-09993-0",
  "categories": [
    "math.GR"
  ],
  "abstract": "This paper enriches the list of known properties of congruence sequences starting from the universal relation and successively performing the operators lower $k$ and lower $t$. Two series of inverse semigroups, namely $\\ker{\\alpha_n}$-is-Clifford semigroups and $\\beta_n$-is-over-$E$-unitary semigroups, are investigated. Two congruences, namely $\\alpha_{n+2}$ and $\\beta_{n+2}$, are found to be the least $\\ker{\\alpha_n}$-is-Clifford and least $\\beta_n$-is-over-$E$-unitary congruences on $S$, respectively. A new system of implications is established for the quasivarieties of inverse semigroups induced by the min network.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-17T14:42:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "inverse semigroup",
      "paper enriches",
      "unitary semigroups",
      "is-clifford semigroups",
      "min network"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}