{
  "abstract": "We show that every countable group $G$ that has Ozawa's property $\\rm PHP$ and contains a non-abelian free subgroup has the following property: the group ring $KG$ is primitive for any field $K$. As a consequence, we deduce that all non-trivial countable linear groups with trivial amenable radical have this property. Along the way, we prove that the class of groups with $\\rm PHP$ enjoys some permanence properties that are of independent interest.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14814",
  "author_total": 1,
  "authors": [
    {
      "name": "Felipe I. Flores"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/17kcf1b7cscwr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14814",
  "fulltext_url": null,
  "id": "17kcf1b7cscwr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14814",
  "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.GR"
    ],
    [
      "arxiv",
      "math.OA"
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      "arxiv",
      "math.RA"
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      "openalex",
      "2610|Advanced Operator Algebra Research"
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  "openalex": "W7213313362",
  "pdf_url": "https://arxiv.org/pdf/2609.14814",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/17kcf1b7cscwr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:45Z",
      "native_id": "2609.14814",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14814"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "PHP decompositions and primitivity of group rings for linear groups",
  "title_text": "PHP decompositions and primitivity of group rings for linear groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:45Z",
  "url": "https://research.draconitic.com/paper/17kcf1b7cscwr",
  "venue": "arXiv",
  "versions": []
}