{
  "abstract": "For any $m$ pairwise commuting matrices $\\{A_i\\}_{i=1}^{m}\\subset \\M_n(\\F)$, we prove $\\dim_\\F \\F[A_1,\\cdots, A_m]\\leq (2^m-1)(n-1)+1$, answering Bergman's question on the existence of a linear bound for a fixed number $m$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.08135",
  "author_total": 4,
  "authors": [
    {
      "name": "Jiamei Li"
    },
    {
      "name": "Caihua Luo"
    },
    {
      "name": "Xu Song"
    },
    {
      "name": "Yilin Zeng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/257s79xac3b5n.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.08135",
  "fulltext_url": null,
  "id": "257s79xac3b5n",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.08135",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.RA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.08135",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/257s79xac3b5n.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2611.08135",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.08135"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Linear bounds and sharp exponential growth for commuting matrix algebra",
  "title_text": "Linear bounds and sharp exponential growth for commuting matrix algebra",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:48Z",
  "url": "https://research.draconitic.com/paper/257s79xac3b5n",
  "venue": "arXiv",
  "versions": []
}