{
  "abstract": "We show that every proper variety of distributive $\\ell$-pregroups is periodic; as a result, the subvariety lattice of the variety of distributive $\\ell$-pregroups decomposes into a disjoint union of bounded intervals each consisting of all properly $n$-periodic varieties, for different $n \\in \\mathbb{Z}^+$. On the way, we study non-periodic (one-generated) subalgebras of $\\mathbf{F}(\\mathbb{Z})$ and show that they either contain a non-periodic idempotent or they contain idempotents of arbitrary big periodicity. The same results holds for non-periodic one-generated subalgebras of $\\mathbf{F}(\\mathbf{J} \\overrightarrow{\\times} \\mathbb{Z})$, where $\\mathbf{J}$ is a chain, generated by a composite element and the resulting idempotents can be taken to be local in the associated wreath product.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.16775",
  "author_total": 2,
  "authors": [
    {
      "name": "Nikolaos Galatos"
    },
    {
      "name": "Simon Santschi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fy32mhh0n7z97.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.16775",
  "fulltext_url": null,
  "id": "fy32mhh0n7z97",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.16775",
  "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.LO"
    ],
    [
      "arxiv",
      "math.RA"
    ],
    [
      "openalex",
      "1703|Advanced Algebra and Logic"
    ]
  ],
  "openalex": "W7221774446",
  "pdf_url": "https://arxiv.org/pdf/2610.16775",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fy32mhh0n7z97.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:16Z",
      "native_id": "2610.16775",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.16775"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Proper varieties of distributive l-pregroups are periodic",
  "title_text": "Proper varieties of distributive l-pregroups are periodic",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:16Z",
  "url": "https://research.draconitic.com/paper/fy32mhh0n7z97",
  "venue": "arXiv",
  "versions": []
}