{
  "abstract": "A variety of universal algebras is called Cross if it is finitely based, finitely generated, and has only finitely many subvarieties. A monoid is aperiodic if all its subgroups are trivial. In the present article, we show that a variety of aperiodic monoids is Cross if and only if it excludes, as subvarieties, a certain list of 22 almost Cross varieties. Consequently, this list of 22 varieties exhausts all almost Cross varieties of aperiodic monoids.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Monatsh. Math. (2026) 211:221-241",
  "arxiv": "2608.06982",
  "author_total": 1,
  "authors": [
    {
      "name": "Sergey V. Gusev"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8csd21krs7p54.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.06982",
  "fulltext_url": null,
  "id": "8csd21krs7p54",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.06982",
  "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.GR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2608.06982",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8csd21krs7p54.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2608.06982",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.06982"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Cross varieties of aperiodic monoids",
  "title_text": "Cross varieties of aperiodic monoids",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/8csd21krs7p54",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1007/s00605-026-02220-3",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}