{
  "abstract": "We study the Kothe radical (the upper nil radical) in the variety of Novikov algebras. We prove that the class of weakly right nilpotent Novikov algebras coincides with the class of r-nil algebras and forms a radical class. We establish that the Kothe radical is a hereditary radical in the variety of Novikov algebras. Furthermore, we obtain a structural description of the Kothe radical as the intersection of ideals whose corresponding quotient algebras are prime K-semisimple algebras. Finally, we construct an example of a prime r-nil Novikov algebra over a field of characteristic p>0, which implies that the Baer radical is strictly contained in the Kothe radical in this case.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.36903",
  "author_total": 1,
  "authors": [
    {
      "name": "Alexander S. Panasenko"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6gewh62bbb7af.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.36903",
  "fulltext_url": null,
  "id": "6gewh62bbb7af",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.36903",
  "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.QA"
    ],
    [
      "arxiv",
      "math.RA"
    ],
    [
      "openalex",
      "2602|Advanced Topics in Algebra"
    ]
  ],
  "openalex": "W7224080565",
  "pdf_url": "https://arxiv.org/pdf/2610.36903",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6gewh62bbb7af.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.36903",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.36903"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The Kothe Radical in Novikov Algebras",
  "title_text": "The Kothe Radical in Novikov Algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/6gewh62bbb7af",
  "venue": "arXiv",
  "versions": []
}