{
  "abstract": "Given a field $\\mathbb{F}$ and an integer $n \\geq 2$, denote by $t_n(\\mathbb{F})$ the greatest possible dimension for a vector space of $n$-by-$n$ matrices over $\\mathbb{F}$ in which every element is triangularizable. It was recently proved that $t_n(\\mathbb{F})=\\frac{n(n+1)}{2}$ if and only if $\\mathbb{F}$ is not quadratically closed, with the possible exception of finite fields with characteristic $2$ and less than $n-1$ elements. In this article, we prove that the equality $t_n(\\mathbb{F})=\\frac{n(n+1)}{2}$ holds for all perfect non-quadratically closed fields with characteristic $2$ -- with the possible exception of fields with cardinality $2$ -- and for these fields we obtain a key result for a future analysis of the spaces that have the critical dimension $t_n(\\mathbb{F})$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.28863",
  "author_total": 1,
  "authors": [
    {
      "name": "Clément de Seguins Pazzis"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/av2rz5sxx7144.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.28863",
  "fulltext_url": null,
  "id": "av2rz5sxx7144",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.28863",
  "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|Rings, Modules, and Algebras"
    ]
  ],
  "openalex": "W7204940410",
  "pdf_url": "https://arxiv.org/pdf/2608.28863",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/av2rz5sxx7144.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2608.28863",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.28863"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Spaces of triangularizable matrices (III): Perfect non-quadratically closed fields with characteristic 2",
  "title_text": "Spaces of triangularizable matrices (III): Perfect non-quadratically closed fields with characteristic 2",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/av2rz5sxx7144",
  "venue": "arXiv",
  "versions": []
}