{
  "abstract": "In this paper, we provide an explicit method for determining the zero set of monic quadratic general polynomials over Cayley--Dickson algebras with any base field of characteristic not equal to $2$, which reduces the problem to finding the roots of univariate polynomials over the base field. For the special case of locally-complex Cayley--Dickson algebras over the reals, we prove that every such polynomial has a root. We prove the existence of right eigenvalues for any $2 \\times 2$ matrix over Cayley's octonions (the real octonion division algebra), and our root-finding method allows the computation of some of the right eigenvalues.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Communications in Mathematics, Volume 35 (2027), Issue 2 (Special issue: European Non-Associative Algebra Seminar) (October 19, 2026) cm:18874",
  "arxiv": "2607.23613",
  "author_total": 3,
  "authors": [
    {
      "name": "Adam Chapman"
    },
    {
      "name": "Ilan Levin"
    },
    {
      "name": "Solomon Vishkautsan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/682c61a3day98.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.23613",
  "fulltext_url": null,
  "id": "682c61a3day98",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.23613",
  "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/2607.23613",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/682c61a3day98.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2607.23613",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.23613"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "General Polynomials and Eigenvalues Over Cayley--Dickson Algebras",
  "title_text": "General Polynomials and Eigenvalues Over Cayley--Dickson Algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/682c61a3day98",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.46298/cm.18874",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}