{
  "abstract": "Let $\\mathbb{F}$ be a finite field and let $G$ be a group such that every finite subgroup of $G$ is cyclic. In this paper we classify the division gradings by cyclic groups on matrix algebras over $\\mathbb{F}$. This yields the classification of the $G$-gradings on these algebras. Moreover if $G$ is abelian we prove that two matrix algebras over $\\mathbb{F}$ with $G$-gradings satisfy the same graded identities if and only if they are isomorphic as graded algebras.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.20113",
  "author_total": 4,
  "authors": [
    {
      "name": "Diogo Diniz"
    },
    {
      "name": "Daniela Martinez Correa"
    },
    {
      "name": "Dimas José Gonçalves"
    },
    {
      "name": "Plamen Koshlukov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/58d68y31hzpwj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.20113",
  "fulltext_url": null,
  "id": "58d68y31hzpwj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.20113",
  "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": "W7222077809",
  "pdf_url": "https://arxiv.org/pdf/2610.20113",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/58d68y31hzpwj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.20113",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.20113"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Identities and isomorphisms of finite graded matrix algebras",
  "title_text": "Identities and isomorphisms of finite graded matrix algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/58d68y31hzpwj",
  "venue": "arXiv",
  "versions": []
}