{
  "abstract": "We construct a complete local Gorenstein ring $R$ of dimension $1$ with a prime ideal $\\mathfrak{p}\\in \\operatorname{Spec}(R)$ such that $R$ is an AB ring, but the localization $R_{\\mathfrak{p}}$ is not an AB ring. This settles the localization problem for AB rings posed by Huneke and Jorgensen in the negative.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.00754",
  "author_total": 2,
  "authors": [
    {
      "name": "Justin Lyle"
    },
    {
      "name": "Saeed Nasseh"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6exh19gnf2svd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.00754",
  "fulltext_url": null,
  "id": "6exh19gnf2svd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.00754",
  "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"
    ],
    [
      "openalex",
      "2602|Commutative Algebra and Its Applications"
    ]
  ],
  "openalex": "W7206189591",
  "pdf_url": "https://arxiv.org/pdf/2609.00754",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6exh19gnf2svd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:04Z",
      "native_id": "2609.00754",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.00754"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A counterexample to the localization problem for AB rings",
  "title_text": "A counterexample to the localization problem for AB rings",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:04Z",
  "url": "https://research.draconitic.com/paper/6exh19gnf2svd",
  "venue": "arXiv",
  "versions": []
}