{
  "id": "2407.00819",
  "version": "v1",
  "published": "2024-06-30T20:18:57.000Z",
  "updated": "2024-06-30T20:18:57.000Z",
  "title": "On canonical number systems and monogenity of pure number fields",
  "authors": [
    "Hamid Ben Yakkou",
    "Brahim Boudine"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $m$ be a rational integer $(m \\neq 0, \\pm 1)$ and consider a pure number field $K = \\mathbb{Q} (\\sqrt[n]{m}) $ with $n \\ge 3$. Most papers discussing the monogenity of pure number fields focus only on the case where $m$ is square-free. In this paper, based on a classical theorem of Ore on the prime ideal decomposition \\cite{MN92, O}, we study the monogenity of $K$ with $m$ is not necessarily square-free. As an application, several examples of the application of monogenic fields to CNS (Canonical Number System) are shown. In this way, our results extend some parts of previously established results \\cite{BFC, BF, HNHCNS}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-30T20:18:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A63",
      "11R04",
      "11A63",
      "11R04",
      "11R16",
      "11R21",
      "11Y40",
      "F.2.2"
    ],
    "keywords": [
      "canonical number system",
      "monogenity",
      "pure number fields focus",
      "prime ideal decomposition",
      "results extend"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}