{
  "abstract": "Let $\\Avar_n$ and $\\VV_n$ be the varieties generated by all $n$-element additively idempotent semirings (ai-semirings) and all $n$-element semirings with commutative addition, respectively, in the signature $(+,\\cdot)$ without constants. We prove that both varieties are finitely based if and only if $n\\leq2$. The five-element case follows from cyclic identities and a structural analysis of products of squares. For $n\\geq6$, each variety contains a finite inherently nonfinitely based ai-semiring. We also prove $\\VV_n\\cap\\AI=\\Avar_n$ for every $n$, where $\\AI$ is the variety of all ai-semirings.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12486",
  "author_total": 2,
  "authors": [
    {
      "name": "Aifa Wang"
    },
    {
      "name": "Lili Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9jxhcgptnc7jn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12486",
  "fulltext_url": null,
  "id": "9jxhcgptnc7jn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.12486",
  "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.RA"
    ],
    [
      "openalex",
      "1703|semigroups and automata theory"
    ]
  ],
  "openalex": "W7221573598",
  "pdf_url": "https://arxiv.org/pdf/2610.12486",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9jxhcgptnc7jn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2610.12486",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12486"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The finite basis problem for varieties generated by all semirings of a fixed order",
  "title_text": "The finite basis problem for varieties generated by all semirings of a fixed order",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/9jxhcgptnc7jn",
  "venue": "arXiv",
  "versions": []
}