{
  "abstract": "Let $d_1,\\ldots,d_r$ be pairwise relatively prime positive square-free integers, with $d_j\\geq2$ for all $1\\leq j\\leq r$. Using elementary matrices and combinatorial mathematics, we give a complete classification of the irreducible $\\mathbb{Z}_+$-modules over the domain $\\mathbb{Z}[d^{\\frac{1}{N_1}}_1,d^{\\frac{1}{N_2}}_2,\\dots,d^{\\frac{1}{N_r}}_r]$, where $N_i \\geq2$ for all $ 1\\leq i \\leq r$. Furthermore, we explicitly construct all of these irreducible $\\mathbb{Z}_+$-modules.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.30905",
  "author_total": 1,
  "authors": [
    {
      "name": "Yue Meng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5xs71df3sqg80.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.30905",
  "fulltext_url": null,
  "id": "5xs71df3sqg80",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.30905",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.RA"
    ],
    [
      "openalex",
      "2602|Rings, Modules, and Algebras"
    ]
  ],
  "openalex": "W7204883983",
  "pdf_url": "https://arxiv.org/pdf/2608.30905",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5xs71df3sqg80.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.30905",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.30905"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Irreducible $\\mathbb{Z}_+$-modules over some $\\mathbb{Z}_+$-rings",
  "title_text": "Irreducible ℤ_+-modules over some ℤ_+-rings",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/5xs71df3sqg80",
  "venue": "arXiv",
  "versions": []
}