{
  "abstract": "A ring is right pure semisimple if every right module is a direct sum of finitely generated modules, and the pure semisimplicity conjecture asserts that every such ring is of finite representation type. In this article, a division ring extension $H\\subseteq T$ is constructed such that the bimodule ${}_HT_T$ has right dimension sequence $(1,2,2,2,\\dots)$ and $T$ is infinite-dimensional as a left $H$-space. The division ring $T$ is the union of the fraction division rings of the nearest-neighbour quantum Laurent algebras with parameter $1/2$, and $H$ is the image of $T$ under a compatible family of conjugations. The extension is controlled by right bases of every length and by two-sided flags of adjacent division subrings, which identify all iterated right duals up to explicit twists. It follows that the triangular ring $\\left(\\begin{smallmatrix}H&T\\\\0&T\\end{smallmatrix}\\right)$ is right pure semisimple but neither left pure semisimple nor of finite representation type, so that the pure semisimplicity conjecture fails.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.39883",
  "author_total": 1,
  "authors": [
    {
      "name": "Junpeng Ren"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/crvg7xykepms6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.39883",
  "fulltext_url": null,
  "id": "crvg7xykepms6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.39883",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.RA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.39883",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/crvg7xykepms6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.39883",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.39883"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A counterexample to the pure semisimplicity conjecture",
  "title_text": "A counterexample to the pure semisimplicity conjecture",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/crvg7xykepms6",
  "venue": "arXiv",
  "versions": []
}