{
  "abstract": "Let $R$ be a ring and $M$ a left $R$-module. We prove that $M$ is an $ω_1$-indexed inverse limit of injective modules with split epimorphic connecting maps, and $M$ is also an $ω$-indexed inverse limit of a stationary tower defined by a split monic endomorphism of one injective module. These constructions answer two questions of Bergman. We then study the class of direct summands of $ω$-indexed inverse limit of injective modules with epimorphic connecting maps. Over a commutative Noetherian ring $R$, they are precisely the Enochs cotorsion modules if and only if $\\operatorname{gldim}R\\leq1$ and $\\operatorname{Spec}R$ is countable.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.36089",
  "author_total": 1,
  "authors": [
    {
      "name": "Chencheng Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cgb216xfnq1f1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.36089",
  "fulltext_url": null,
  "id": "cgb216xfnq1f1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.36089",
  "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"
    ],
    [
      "arxiv",
      "math.RA"
    ],
    [
      "openalex",
      "2602|Rings, Modules, and Algebras"
    ]
  ],
  "openalex": "W7214983720",
  "pdf_url": "https://arxiv.org/pdf/2609.36089",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cgb216xfnq1f1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.36089",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.36089"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A note on inverse limits of injective modules",
  "title_text": "A note on inverse limits of injective modules",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/cgb216xfnq1f1",
  "venue": "arXiv",
  "versions": []
}