{
  "id": "2005.01915",
  "version": "v1",
  "published": "2020-05-05T02:18:56.000Z",
  "updated": "2020-05-05T02:18:56.000Z",
  "title": "On integral basis of pure number fields",
  "authors": [
    "Anuj Jakhar",
    "Sudesh K. Khanduja",
    "Neeraj Sangwan"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $K=\\mathbb{Q}(\\sqrt[n]{a})$ be an extension of degree $n$ of the field $\\Q$ of rational numbers, where the integer $a$ is such that for each prime $p$ dividing $n$ either $p\\nmid a$ or the highest power of $p$ dividing $a$ is coprime to $p$; this condition is clearly satisfied when $a, n$ are coprime or $a$ is squarefree. The present paper gives explicit construction of an integral basis of $K$ along with applications. This construction of an integral basis of $K$ extends a result proved in [J. Number Theory, {173} (2017), 129-146] regarding periodicity of integral bases of $\\mathbb{Q}(\\sqrt[n]{a})$ when $a$ is squarefree.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-05T02:18:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R04",
      "11R29"
    ],
    "keywords": [
      "integral basis",
      "pure number fields",
      "highest power",
      "explicit construction",
      "rational numbers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}