{
  "abstract": "For each pair of integers $m\\ge 1$ and $n\\ge 2$, we construct a finite inverse semigroup $S_{m,n}\\subseteq M_m(\\mathbb{C})$ and explicitly determine its marginal inverse subsemigroup $M_{x^n}(S_{m,n})$ associated with the word $x^n$. We prove that the three conditions $\\sim_{x^n}=\\equiv_{x^n}$ on $S_{m,n}$, $M_{x^n}(S_{m,n})\\trianglelefteq S_{m,n}$, and $m\\le n$ are equivalent. As a consequence, we answer Problem 11 of Araújo, Araújo and Kinyon in [1]. Moreover, for a word $ω$ in any inverse semigroup $S$, we prove that $\\sim_ω=\\equiv_ω$ if and only if $M_ω(S)\\trianglelefteq S$ and $\\sim_ω$ is invariant under inversion.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.05078",
  "author_total": 2,
  "authors": [
    {
      "name": "Bing Duan"
    },
    {
      "name": "Jizhi Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c1pfxrjtejdhx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.05078",
  "fulltext_url": null,
  "id": "c1pfxrjtejdhx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.05078",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.RT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.05078",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c1pfxrjtejdhx.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:29Z",
      "native_id": "2611.05078",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.05078"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Normality of marginal inverse subsemigroups in inverse semigroups",
  "title_text": "Normality of marginal inverse subsemigroups in inverse semigroups",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/c1pfxrjtejdhx",
  "venue": "arXiv",
  "versions": []
}