{
  "abstract": "Let $R$ be a commutative ring and $Φ$ an inverse family of ideals with greatest proper member $\\mathcal{L}$. We introduce and study $Φ$-reduced and $Φ$-coreduced modules, extending the corresponding notions for powers of a single ideal. We show that, on these classes of modules, the generalized torsion and completion functors associated with $Φ$ are determined by $\\mathcal{L}$. We establish characterizations and closure properties of these modules and obtain a Greenlees-May type adjunction and a Matlis-Greenlees-May type characterization. When $Φ$ is a system of ideals, we further investigate the radicality of the generalized torsion functor and derive associated torsion theories on suitable Serre subcategories. These results provide a module-theoretic framework for studying generalized torsion and completion with respect to families of ideals.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.30091",
  "author_total": 2,
  "authors": [
    {
      "name": "Sholastica Luambano"
    },
    {
      "name": "David Ssevviiri"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3ya8czz8p033a.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.30091",
  "fulltext_url": null,
  "id": "3ya8czz8p033a",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.30091",
  "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": "W7214313010",
  "pdf_url": "https://arxiv.org/pdf/2609.30091",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3ya8czz8p033a.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:57Z",
      "native_id": "2609.30091",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.30091"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Reduced and coreduced modules with respect to inverse families of ideals",
  "title_text": "Reduced and coreduced modules with respect to inverse families of ideals",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:57Z",
  "url": "https://research.draconitic.com/paper/3ya8czz8p033a",
  "venue": "arXiv",
  "versions": []
}