{
  "abstract": "This paper deals with certain classes of modules under module-finite extensions. Let $φ: R\\hookrightarrow S$ be a module-finite extension between commutative Noetherian local rings. We investigate the transfer of Artinian module structures and attached primes between $R$ and $S$. We clarify the behavior of local cohomology modules as well as certain structures of finitely generated $S$-modules under the restriction of scalars to $R$ via $φ$. We show that $R$ is a quotient of a Cohen-Macaulay local ring if and only if so is $S$. As an application, we characterize the structure of Nagata's idealization. Using Macaulayfication of algebraic varieties and idealization, we give an example to illustrate the results.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Acta Mathematica Vietnamica, 2026",
  "arxiv": "2609.11003",
  "author_total": 1,
  "authors": [
    {
      "name": "Tran Do Minh Chau"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/90dyd6spcv6sc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.11003",
  "fulltext_url": null,
  "id": "90dyd6spcv6sc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.11003",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AC"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.11003",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/90dyd6spcv6sc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2609.11003",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.11003"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The transfer of Artinian and Cohen-Macaulay properties under module-finite extensions",
  "title_text": "The transfer of Artinian and Cohen-Macaulay properties under module-finite extensions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/90dyd6spcv6sc",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1007/s40306-026-00620-z",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}