{
  "abstract": "Let $M$ denote a module over a local Noetherian ring $(R,\\mathfrak{m})$ with residue field $\\Bbbk$ and its injective hull $E_R$. Let $D_R(\\cdot) = \\operatorname{Hom}_R(\\cdot,E_R)$ denote the Matlis duality functor. Then $M$ is called Matlis reflexive whenever the injection $M \\to D_R^2(M)$ is an isomorphism. The following results are proved: (1) For an ideal of $R$ a reflexive module is quasi-complete, generalizing part of Belshoff's results (see \\cite{Br}). (2) We improve Zöschinger's numerical criterion for Matlis reflexivity (see \\cite{Zh2}). (3) As shown by Enochs (see \\cite{Ee}) for a prime ideal and the injective hull $E_R(R/\\mathfrak{p})$ it follows that $D_R(E_R(R/\\mathfrak{p}))$ is the completion of a free $R_{\\mathfrak{p}}$-module of rank $τ_{\\mathfrak{p}}$, the Enochs number of $\\mathfrak{p}$. We characterize when $τ_{\\mathfrak{p}} = 1$, extending author's result (see \\cite{Sp16}).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.25167",
  "author_total": 1,
  "authors": [
    {
      "name": "Peter Schenzel"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e34jz27s5r3g8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.25167",
  "fulltext_url": null,
  "id": "e34jz27s5r3g8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.25167",
  "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.AC"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.25167",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e34jz27s5r3g8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2609.25167",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.25167"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Notes on Matlis reflexive modules",
  "title_text": "Notes on Matlis reflexive modules",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/e34jz27s5r3g8",
  "venue": "arXiv",
  "versions": []
}