{
  "abstract": "We show that the six-element additively idempotent semiring $B_2^1$ is inherently nonfinitely based. More precisely, for every positive integer $n$, we construct an infinite additively idempotent semiring, generated by at most $(6n+8)^2$ elements, that satisfies every $n$-variable identity of $B_2^1$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12491",
  "author_total": 3,
  "authors": [
    {
      "name": "Miao Miao Ren"
    },
    {
      "name": "Meng Ya Yue"
    },
    {
      "name": "Yi Lin Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ctv5yvcr192r3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12491",
  "fulltext_url": null,
  "id": "ctv5yvcr192r3",
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  "landing_url": "https://arxiv.org/abs/2610.12491",
  "language": null,
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  "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"
    ],
    [
      "arxiv",
      "math.RA"
    ],
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      "openalex",
      "1703|semigroups and automata theory"
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  "openalex": "W7221539052",
  "pdf_url": "https://arxiv.org/pdf/2610.12491",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ctv5yvcr192r3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2610.12491",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12491"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The six-element additively idempotent semiring $B_2^1$ is inherently nonfinitely based",
  "title_text": "The six-element additively idempotent semiring B_2^1 is inherently nonfinitely based",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/ctv5yvcr192r3",
  "venue": "arXiv",
  "versions": []
}