{
  "abstract": "Let $R$ be a one-dimensional commutative Noetherian ring with a unique minimal prime $\\mathfrak p$ such that $D=R/\\mathfrak p$ is a principal ideal domain. We give a complete characterization of the iso-Artinian property in this class, that is, the following conditions are equivalent: $R$ is iso-Artinian; $\\mathfrak pR_{\\mathfrak p}=0$; $len_R(\\mathfrak p)<\\infty$; $\\mathfrak p/\\mathfrak p^2$ is torsion over $D$. As a consequence, we completely answer the Question~3.9 of Daneshvar and Divaani-Aazar: under their hypotheses $Min R\\subsetneq Ass R$, the ring is iso-Artinian precisely when its nilradical has finite length, and it is non-iso-Artinian precisely when the conormal module has positive rank.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14331",
  "author_total": 3,
  "authors": [
    {
      "name": "Xiaolei Zhang"
    },
    {
      "name": "Ran Yan"
    },
    {
      "name": "Wei Qi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/716c436aghf1w.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14331",
  "fulltext_url": null,
  "id": "716c436aghf1w",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14331",
  "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": "W7213346390",
  "pdf_url": "https://arxiv.org/pdf/2609.14331",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/716c436aghf1w.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.14331",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14331"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On the iso-Artinianness of one-dimensional Noetherian rings",
  "title_text": "On the iso-Artinianness of one-dimensional Noetherian rings",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/716c436aghf1w",
  "venue": "arXiv",
  "versions": []
}