{
  "abstract": "For every field~$\\Bbbk$, we construct a non-nilpotent nil algebra~$A$ whose Lie algebra $A^{(-)}$ is generated by ten elements. For $\\Bbbk = \\mathbb Z_p$, its adjoint group can also be generated by ten elements. Moreover, for every field $\\Bbbk$ algebraic over its prime subfield, we construct a finitely presented algebra $B$ over $\\Bbbk$ whose Jacobson radical is not nil. These results were found with the assistance of Aristotle (Harmonic).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.34463",
  "author_total": 1,
  "authors": [
    {
      "name": "Vsevolod Gubarev"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cy8a2ry6mv61b.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.34463",
  "fulltext_url": null,
  "id": "cy8a2ry6mv61b",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.34463",
  "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",
      "2602|Advanced Topics in Algebra"
    ]
  ],
  "openalex": "W7223817223",
  "pdf_url": "https://arxiv.org/pdf/2610.34463",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cy8a2ry6mv61b.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.34463",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.34463"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "New results on nil rings",
  "title_text": "New results on nil rings",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/cy8a2ry6mv61b",
  "venue": "arXiv",
  "versions": []
}