{
  "abstract": "Let $R$ be a commutative ring with exactly $n\\ge 2$ maximal ideals and let $k\\ge 2$. We study the minimal $k$-uniform comaximal hypergraph $\\mathcal{H}_k(R)$, whose vertices are the nonunits outside the Jacobson radical and whose edges are the irredundant $k$-element comaximal families. For $2\\le k\\le n$ we show that $\\mathcal{H}_k(R)$ is a blow-up of the hypergraph of irredundant $k$-coverings of $\\{1,\\dots,n\\}$, and that its reduced form reconstructs the maximal ideals up to permutation; for $k>n$ there are no edges. We obtain a general description of $\\mathrm{Aut}(\\mathcal{H}_k(R))$ and characterize isomorphisms of such hypergraphs. For $3\\le k\\le n$ its automorphism group properly contains that of the comaximal graph, and for finite rings with $n\\ge 3$ and every $2\\le k\\le n$, $\\mathcal{H}_k(R)$ has the same isomorphism invariants as the comaximal graph, namely $|J(R)|$ and $R/J(R)$. The case $k=2$ recovers and extends the automorphism results for comaximal graphs obtained previously. We also compare the minimal and non-minimal comaximal hypergraphs and identify a condition under which the latter has the same automorphism group and isomorphism invariants as the comaximal graph. The same method determines the vertex set and the automorphism group of the $k$-zero-divisor hypergraph of a product of integral domains, and shows that for finite products of finite fields this hypergraph determines the ring.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.07992",
  "author_total": 1,
  "authors": [
    {
      "name": "Elham Mehdi-Nezhad"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3ka2eb8phcgy6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.07992",
  "fulltext_url": null,
  "id": "3ka2eb8phcgy6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.07992",
  "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.AC"
    ],
    [
      "arxiv",
      "math.CO"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.07992",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3ka2eb8phcgy6.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2611.07992",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.07992"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Isomorphisms and automorphisms of minimal comaximal hypergraphs of commutative rings",
  "title_text": "Isomorphisms and automorphisms of minimal comaximal hypergraphs of commutative rings",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:48Z",
  "url": "https://research.draconitic.com/paper/3ka2eb8phcgy6",
  "venue": "arXiv",
  "versions": []
}