{
  "abstract": "Let $\\mathbb{F}_{q^n}$ be a finite field where $q=p^l$ ($p$ is a prime) and a Dickson nearfield $R$ associated to the field. In this note we investigate the basic properties of the generalized distributive set $D(a,b)$ where $a,b\\in R$. The set is well-known when $n=1, 2$. For $n>2$, we characterize when $D(a,b)$ is a subfield of $\\mathbb{F}_{q^n}$. Furthermore we find the unique largest subfield of $\\mathbb{F}_{q^n}$ contained in $D(a,b)$. We also provide a condition to guarantee that $D(a,b)$ is not a subfield of $\\mathbb{F}_{q^n}$. We end the note by posing the question of when $D(a,b)$, as a space over $\\mathbb{F}_p$, has a primitive normal basis.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10228",
  "author_total": 1,
  "authors": [
    {
      "name": "K. S. Enoch Lee"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/82ehqfrqg4k8f.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10228",
  "fulltext_url": null,
  "id": "82ehqfrqg4k8f",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10228",
  "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|Rings, Modules, and Algebras"
    ]
  ],
  "openalex": "W7212164156",
  "pdf_url": "https://arxiv.org/pdf/2609.10228",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/82ehqfrqg4k8f.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:15Z",
      "native_id": "2609.10228",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10228"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A note on generalized distributive sets of a finite Dickson nearfield",
  "title_text": "A note on generalized distributive sets of a finite Dickson nearfield",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:15Z",
  "url": "https://research.draconitic.com/paper/82ehqfrqg4k8f",
  "venue": "arXiv",
  "versions": []
}