{
  "id": "1902.03692",
  "version": "v1",
  "published": "2019-02-11T01:04:25.000Z",
  "updated": "2019-02-11T01:04:25.000Z",
  "title": "Generators for the $C^m$-closures of Ideals",
  "authors": [
    "Charles Fefferman",
    "Garving K. Luli"
  ],
  "comment": "47 pages, see also the related article \"Solutions to a System of Equations for $C^m$ Functions\"",
  "categories": [
    "math.CA",
    "math.AC",
    "math.AG",
    "math.RA"
  ],
  "abstract": "Let $\\mathscr{R}$ denote the ring of real polynomials on $\\mathbb{R}^{n}$. Fix $m\\geq 0$, and let $A_{1},\\cdots ,A_{M}\\in \\mathscr{R}$. The $ C^{m}$-closure of $\\left( A_{1},\\cdots ,A_{M}\\right) $, denoted here by $ \\left[ A_{1},\\cdots ,A_{M};C^{m}\\right] $, is the ideal of all $f\\in \\mathscr{R}$ expressible in the form $f=F_{1}A_{1}+\\cdots +F_{M}A_{M}$ with each $F_{i}\\in C^{m}\\left( \\mathbb{R}^{n}\\right) $. In this paper we exhibit an algorithm to compute generators for $\\left[ A_{1},\\cdots ,A_{M};C^{m}\\right] $.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-11T01:04:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "generators",
      "real polynomials"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 47,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}