{
  "id": "2212.05840",
  "version": "v1",
  "published": "2022-12-12T11:57:12.000Z",
  "updated": "2022-12-12T11:57:12.000Z",
  "title": "Discriminant and integral basis of pure nonic fields",
  "authors": [
    "Anuj Jakhar",
    "Neeraj Sangwan"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $K = \\Q(\\theta)$ be an algebraic number field with $\\theta$ satisfying an irreducible polynomial $x^{9} - a$ over the field $\\Q$ of rationals and $\\Z_K$ denote the ring of algebraic integers of $K$. In this article, we provide the exact power of each prime which divides the index of the subgroup $\\Z[\\theta]$ in $\\Z_K$. Further, we give a $p$-integral basis of $K$ for each prime $p$. These $p$-integral bases lead to a construction of an integral basis of $K$ which is illustrated with examples.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-12T11:57:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "integral basis",
      "pure nonic fields",
      "discriminant",
      "algebraic number field",
      "algebraic integers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}