{
  "abstract": "Let $A$ be a split finite-dimensional algebra over a field whose radical $J$ satisfies $J^3=0$, and let $s$ be the number of isomorphism classes of simple $A$-modules. We prove that a non-projective module $M$ with ${\\rm Ext}_A^i(M,A)=0$ for all $i>0$ has a non-zero self-extension in some degree between $1$ and $3s+1$. In particular, $A$ satisfies the Auslander--Reiten conjecture, which asserts that every self-orthogonal generator is projective. As a consequence, every finite-dimensional algebra over an algebraically closed field with radical cube zero satisfies the Auslander-Reiten conjecture.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.08679",
  "author_total": 2,
  "authors": [
    {
      "name": "Xiaojin Zhang"
    },
    {
      "name": "Panyue Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/18eghymkgpy8b.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.08679",
  "fulltext_url": null,
  "id": "18eghymkgpy8b",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.08679",
  "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.CT"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7211996131",
  "pdf_url": "https://arxiv.org/pdf/2609.08679",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/18eghymkgpy8b.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.08679",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.08679"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The Auslander-Reiten conjecture for algebras with radical cube zero",
  "title_text": "The Auslander-Reiten conjecture for algebras with radical cube zero",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/18eghymkgpy8b",
  "venue": "arXiv",
  "versions": []
}