{
  "id": "2205.05035",
  "version": "v1",
  "published": "2022-05-10T16:49:34.000Z",
  "updated": "2022-05-10T16:49:34.000Z",
  "title": "Graded rings associated to valuations and direct limits",
  "authors": [
    "Caio Henrique Silva de Souza",
    "Josnei Antonio Novacoski",
    "Mark Spivakovsky"
  ],
  "categories": [
    "math.AC"
  ],
  "abstract": "In this paper, we study the structure of the graded algebra associated to a limit key polynomial $Q_n$ in terms of the key polynomials that define $Q_n$. In order to do that, we use direct limits. In general, we describe the direct limit of a family of graded rings associated to a totally ordered set of valuations. As an example, we describe the graded ring associated to a valuation-algebraic valuation as a direct limit of graded rings associated to residue-transcendental valuations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-05-10T16:49:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "direct limit",
      "graded ring",
      "residue-transcendental valuations",
      "polynomial",
      "valuation-algebraic valuation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}