{
  "abstract": "Jiao and Ren proved that the varieties generated by the matrix semirings $\\M_n(S_7)$ form an ascending chain of nonfinitely based varieties, and asked whether consecutive members are equal for all $n\\geq2$. We give a negative answer by exhibiting an identity in five variables that holds in $\\M_2(S_7)$ and fails in $\\M_3(S_7)$. Consequently, $\\V(\\M_2(S_7))$ is a proper subvariety of $\\V(\\M_n(S_7))$ for every $n\\geq3$. The proof uses the cubic-power property established by Jiao and Ren and a description of products equal to the constant matrix $[a]_n$. The identity forces two distinct indices to exhaust the index set in dimension two; an additional index yields an explicit counterexample in dimension three.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.13981",
  "author_total": 3,
  "authors": [
    {
      "name": "Lili Wang"
    },
    {
      "name": "Jiewei Zhang"
    },
    {
      "name": "Aifa Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6pm9y4h71yh50.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.13981",
  "fulltext_url": null,
  "id": "6pm9y4h71yh50",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.13981",
  "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.RA"
    ],
    [
      "openalex",
      "1703|semigroups and automata theory"
    ]
  ],
  "openalex": "W7221794961",
  "pdf_url": "https://arxiv.org/pdf/2610.13981",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6pm9y4h71yh50.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.13981",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.13981"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A separating identity for matrix semirings over $S_7$",
  "title_text": "A separating identity for matrix semirings over S_7",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/6pm9y4h71yh50",
  "venue": "arXiv",
  "versions": []
}