{
  "abstract": "We study $n$-torsionfree objects in abelian categories with enough projectives. Frobenius functors preserve $n$-torsionfreeness, and faithful ones reflect it. We prove that stabilization of the torsionfree filtration implies weak Gorensteinness. For Frobenius extensions satisfying a generator condition, we compare the terms of minimal injective resolutions and obtain transfer of Auslander-type conditions and of the Auslander--Gorenstein conjecture. We also compute a family of non-Gorenstein algebras whose torsionfree filtrations stabilize at level two and contain explicit nonprojective Gorenstein projective modules.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.25539",
  "author_total": 1,
  "authors": [
    {
      "name": "Zhibing Zhao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d83wj8af8k81d.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.25539",
  "fulltext_url": null,
  "id": "d83wj8af8k81d",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.25539",
  "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.RA"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7214091443",
  "pdf_url": "https://arxiv.org/pdf/2609.25539",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d83wj8af8k81d.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2609.25539",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.25539"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Frobenius functors and $n$-torsionfree objects",
  "title_text": "Frobenius functors and n-torsionfree objects",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/d83wj8af8k81d",
  "venue": "arXiv",
  "versions": []
}