{
  "abstract": "Let $G$ be an arbitrary group and let $\\mathbb{F}$ be a finite field. In this paper, we determine bases for the $T_G$-ideals of graded polynomial identities of the algebra $M_2(\\mathbb{F})$ for all possible $G$-gradings. The bases obtained consist of finitely many non-trivial graded identities, and are finite whenever $G$ is finite.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Communications in Mathematics, Volume 34 (2026), Issue 2 (Special issue: Latin American mathematics) (October 6, 2026) cm:18621",
  "arxiv": "2605.30494",
  "author_total": 3,
  "authors": [
    {
      "name": "Diogo Diniz"
    },
    {
      "name": "Eduardo Pinto da Fonsêca"
    },
    {
      "name": "Luis Filipe Ramos"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3cff82ept1cmq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.30494",
  "fulltext_url": null,
  "id": "3cff82ept1cmq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.30494",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.RA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2605.30494",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3cff82ept1cmq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2605.30494",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.30494"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Graded identities for matrix algebras of order two over a finite field",
  "title_text": "Graded identities for matrix algebras of order two over a finite field",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/3cff82ept1cmq",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.46298/cm.18621",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}