{
  "abstract": "It was conjectured that every integral domain $D$ satisfies $\\dim\\operatorname{Int}(D) \\leq \\dim D[X]$. We disprove this conjecture and, more strongly, classify all pairs for which both dimensions are finite. Writing $m=\\dim D[X]$ and $n=\\dim\\operatorname{Int}(D)$, the pairs that occur are precisely $\\{(1,1),(2,2)\\}\\ \\cup\\ \\{(m,n)\\in\\mathbb Z_{>0}^{2}:m\\geq3,\\ n\\geq m-1\\}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.00115",
  "author_total": 2,
  "authors": [
    {
      "name": "Viet-Hoang Tran"
    },
    {
      "name": "Tan M. Nguyen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/21mmv6cesxmde.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.00115",
  "fulltext_url": null,
  "id": "21mmv6cesxmde",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.00115",
  "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"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.00115",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/21mmv6cesxmde.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.00115",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.00115"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On the Krull dimensions of rings of integer-valued polynomials and polynomial rings",
  "title_text": "On the Krull dimensions of rings of integer-valued polynomials and polynomial rings",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/21mmv6cesxmde",
  "venue": "arXiv",
  "versions": []
}