{
  "id": "1909.10860",
  "version": "v1",
  "published": "2019-09-24T13:03:40.000Z",
  "updated": "2019-09-24T13:03:40.000Z",
  "title": "On the computation of overorders",
  "authors": [
    "Tommy Hofmann",
    "Carlo Sircana"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "The computation of a maximal order of an order in a semisimple algebra over a global field is a classical well-studied problem in algorithmic number theory. In this paper we consider the related problems of computing all minimal overorders as well as all overorders of a given order. We use techniques from algorithmic representation theory and the theory of minimal integral ring extensions to obtain efficient and practical algorithms, whose implementation is publicly available.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-09-24T13:03:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11Y40",
      "11R04"
    ],
    "keywords": [
      "computation",
      "minimal integral ring extensions",
      "algorithmic representation theory",
      "algorithmic number theory",
      "minimal overorders"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}