{
  "abstract": "We present the complete classification of non-isomorphic complex $3$-dimensional unital commutative algebras. Every such algebra decomposes canonically as $\\mathbb Ce_1\\oplus V$, where $e_1$ is the unit and $V$ is the kernel of the trace form; the induced traceless $2$-dimensional commutative algebra on $V$ is one of four algebras, and the classification reduces to the classification of symmetric bilinear forms on $V$ up to the automorphisms of this kernel. The answer consists of six algebras, three one-parameter families, one two-parameter family and one three-parameter family.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.18689",
  "author_total": 2,
  "authors": [
    {
      "name": "Maqpal Eraliyeva"
    },
    {
      "name": "Ivan Kaygorodov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fm9xt3apjxcba.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.18689",
  "fulltext_url": null,
  "id": "fm9xt3apjxcba",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.18689",
  "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": "W7221748082",
  "pdf_url": "https://arxiv.org/pdf/2610.18689",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fm9xt3apjxcba.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:20Z",
      "native_id": "2610.18689",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.18689"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Classification of $3$-dimensional unital commutative algebras",
  "title_text": "Classification of $3$-dimensional unital commutative algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:20Z",
  "url": "https://research.draconitic.com/paper/fm9xt3apjxcba",
  "venue": "arXiv",
  "versions": []
}