{
  "id": "1305.6781",
  "version": "v4",
  "published": "2013-05-29T12:46:34.000Z",
  "updated": "2017-07-18T02:45:33.000Z",
  "title": "Generators for abelian extensions of number fields",
  "authors": [
    "Ja Kyung Koo",
    "Dong Hwa Shin"
  ],
  "comment": "We will not publish this paper",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $U/L$ be a finite abelian extension of number fields. We first construct a universal primitive generator of $U$ over $L$ whose relative trace to any intermediate field $F$ becomes a generator of $F$ over $L$, too. We also develop a similar argument in terms of norm. As its examples we investigate towers of ray class fields over imaginary quadratic fields. And, we further present a new method of finding a normal element for the extension $U/L$.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-07-04T02:44:30.000Z",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v4",
      "updated": "2017-07-18T02:45:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "12F05",
      "11G16"
    ],
    "keywords": [
      "number fields",
      "finite abelian extension",
      "ray class fields",
      "imaginary quadratic fields",
      "similar argument"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1305.6781K"
    }
  }
}