{
  "id": "2102.01967",
  "version": "v1",
  "published": "2021-02-03T09:37:12.000Z",
  "updated": "2021-02-03T09:37:12.000Z",
  "title": "On monogenity of certain pure number fields defined by $x^{p^r}-m$",
  "authors": [
    "Hamid Ben Yakkou",
    "Lhoussain El Fadil"
  ],
  "comment": "Submitted. arXiv admin note: text overlap with arXiv:2006.11230",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $K = \\mathbb{Q} (\\alpha) $ be a pure number field generated by a complex root $\\alpha$ a monic irreducible polynomial $ F(x) = x^{p^r} -m$, with $ m \\neq 1 $ is a square free rational integer, $p$ is a rational prime integer, and $r$ is a positive integer. In this paper, we study the monogenity of $K$. We prove that if {{$\\nu_p(m^p-m)=1$}}, then $K$ is monogenic. But if $r\\ge p$ and {$\\nu_p(m^{p}-m)> p$}, then $K$ is not monogenic. Some illustrating examples are given.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-03T09:37:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R04",
      "11R16",
      "11R21"
    ],
    "keywords": [
      "pure number field",
      "monogenity",
      "square free rational integer",
      "rational prime integer",
      "complex root"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}