{
  "id": "2111.05899",
  "version": "v1",
  "published": "2021-11-10T19:43:13.000Z",
  "updated": "2021-11-10T19:43:13.000Z",
  "title": "On power integral bases of certain pure number fields defined by $X^{60}-m$",
  "authors": [
    "Lhoussain El Fadil",
    "Omar Kchit",
    "Hanan Choulli"
  ],
  "comment": "Submitted. arXiv admin note: substantial text overlap with arXiv:2106.01252, arXiv:2106.00004",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $K$ be a pure number field generated by a complex root of a monic irreducible polynomial $F(x)=x^{60}-m\\in \\mathbb{Z}[x]$, with $m\\neq \\pm1$ a square free integer. In this paper, we study the monogeneity of $K$. We prove that if $m\\not\\equiv 1\\md{4}$, $m\\not\\equiv \\mp 1 \\md{9} $ and $\\overline{m}\\not\\in\\{\\mp 1,\\mp 7\\} \\md{25}$, then $K$ is monogenic. But if $m\\equiv 1\\md{4}$, $m\\equiv \\mp1 \\md{9}$, or $m\\equiv \\mp 1\\md{25}$, then $K$ is not monogenic. Our results are illustrated by examples.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-11-10T19:43:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R04",
      "11Y40",
      "11R21",
      "C.m"
    ],
    "keywords": [
      "pure number field",
      "power integral bases",
      "square free integer",
      "complex root",
      "monic irreducible polynomial"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}