{
  "abstract": "Let $K$ be an infinite field of characteristic $2$. It is well known that the Lie algebra $\\mathfrak{gl}_2(K)=M_2(K)^{(-)}$ of all $2\\times 2$ matrices does not admit a finite basis of polynomial identities. Similarly, the finite basis problem for the associative algebra $M_2(K)$ remains open. In this note, we obtain two multilinear identities of degree $5$ for $M_2(K)$ and prove that, together with the standard polynomial of degree $4$, they generate all multilinear identities of degree up to $7$. Moreover, we prove that none of the three generators can be omitted.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.25362",
  "author_total": 1,
  "authors": [
    {
      "name": "Iritan Ferreira dos Santos"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/94e5w5v364v7y.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.25362",
  "fulltext_url": null,
  "id": "94e5w5v364v7y",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.25362",
  "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.RA"
    ],
    [
      "openalex",
      "2602|Advanced Topics in Algebra"
    ]
  ],
  "openalex": "W7214083305",
  "pdf_url": "https://arxiv.org/pdf/2609.25362",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/94e5w5v364v7y.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2609.25362",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.25362"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On multilinear polynomial identities for $2\\times2$ matrices in characteristic $2$",
  "title_text": "On multilinear polynomial identities for 2×2 matrices in characteristic $2$",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/94e5w5v364v7y",
  "venue": "arXiv",
  "versions": []
}