{
  "abstract": "A polynomial Krull domain is a Krull domain contained between $\\mathbb Z[X]$ and $\\mathbb Q[X]$. The domains of this class are precisely the Noetherian integrally closed domains between these polynomial rings by a result of Heinzer, and they have been recently classified by Chang and the second author of this paper as rings of polynomials which are integer-valued over a finite set of ultrametric balls in $\\mathbb C_p$, as $p$ ranges through the set of primes in $\\mathbb Z$. We show here that every ideal class of a polynomial Krull domain contains a prime ideal. Furthermore, given such a Krull domain $R$, we prove that there exists a polynomial Krull domain $R'$ that is Dedekind, contains $R$ and has the same class group as $R$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.38457",
  "author_total": 2,
  "authors": [
    {
      "name": "Djamila Ait Elhadi"
    },
    {
      "name": "Giulio Peruginelli"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8scqc69keng9p.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.38457",
  "fulltext_url": null,
  "id": "8scqc69keng9p",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.38457",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AC"
    ],
    [
      "arxiv",
      "math.NT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.38457",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8scqc69keng9p.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.38457",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.38457"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Class groups of polynomial Krull domains",
  "title_text": "Class groups of polynomial Krull domains",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/8scqc69keng9p",
  "venue": "arXiv",
  "versions": []
}