{
  "abstract": "Let $R$ be an integral domain and let $w$ denote the $w$-operation on $R$. A nonzero GV-torsion-free $R$-module $M$ is called $w$-secondary if, for every $r\\in R$, either $M/rM$ is GV-torsion or $r^nM=0$ for some $n\\in\\N$. A $w$-module $M$ is said to admit a $w$-secondary representation if $M=(N_1+\\cdots+N_n)_w$, where each $N_i$ is a $w$-secondary submodule of $M$. Such a representation is called minimal if the ideals $P_i=\\sqrt{\\Ann_R(N_i)}$ are pairwise distinct, and $M$ is called $w$-representable if it admits such a representation. If the sum can be chosen direct, then $M$ is called strongly $w$-representable. We characterize $w$-secondary modules and investigate their localization and $w$-closure properties. For a nonfield domain $R$, we prove that $R$ is $t$-almost Dedekind if and only if $\\wdim R=1$ and every $w$-representable $w$-module is locally strongly $w$-representable: each of its nonzero localizations at maximal $w$-ideals is strongly representable. Global strong $w$-representability is retained when all the radical annihilators in the representation are nonzero.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.16685",
  "author_total": 3,
  "authors": [
    {
      "name": "Hwankoo Kim"
    },
    {
      "name": "Hyungtae Baek"
    },
    {
      "name": "Haleh Hamdi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1s6dhj4vyzmkb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.16685",
  "fulltext_url": null,
  "id": "1s6dhj4vyzmkb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.16685",
  "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|Rings, Modules, and Algebras"
    ]
  ],
  "openalex": "W7221828286",
  "pdf_url": "https://arxiv.org/pdf/2610.16685",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1s6dhj4vyzmkb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.16685",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.16685"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Characterizations of t-Almost Dedekind Domains via w-Secondary Modules",
  "title_text": "Characterizations of t-Almost Dedekind Domains via w-Secondary Modules",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/1s6dhj4vyzmkb",
  "venue": "arXiv",
  "versions": []
}