{
  "id": "2106.01252",
  "version": "v1",
  "published": "2021-06-02T16:07:10.000Z",
  "updated": "2021-06-02T16:07:10.000Z",
  "title": "On power integral bases of certain pure number fields defined by $x^{2^u\\cdot3^v}-m$",
  "authors": [
    "H. Ben Yakkou",
    "Lhoussain El Fadil",
    "A. Najim"
  ],
  "comment": "Submitted. arXiv admin note: substantial text overlap with arXiv:2102.01967, arXiv:2106.00004, arXiv:2006.11230",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $K = \\mathbb{Q} (\\alpha) $ be a pure number field generated by a complex root $\\alpha$ of a monic irreducible polynomial $ F(x) = x^{2^u\\cdot 3^v}-m$, with $m \\neq \\pm 1$ a square free rational integer, $u$, and $v$ two positive integers. In this paper, we study the monogenity of $K$. The case $u=0$ or $v=0$ has been previously studied. We prove that if $m\\not\\equiv 1$ (mod4) and $m\\not\\equiv \\pm 1$ (mod9), then $K$ is monogenic. But if $m\\equiv 1$ (mod4) or $m\\equiv 1$ (mod9), then $K$ is not monogenic. Some illustrating examples are given too.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-02T16:07:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R04",
      "11R16",
      "11R21",
      "G.0"
    ],
    "keywords": [
      "pure number field",
      "power integral bases",
      "square free rational integer",
      "complex root",
      "monic irreducible polynomial"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}