{
  "id": "1608.03728",
  "version": "v1",
  "published": "2016-08-12T09:09:23.000Z",
  "updated": "2016-08-12T09:09:23.000Z",
  "title": "On the Surjectivity of Certain Maps",
  "authors": [
    "C. P. Anil Kumar"
  ],
  "comment": "29 pages",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We prove in this article the surjectivity of three maps. We prove in Theorem $1$ the surjectivity of the chinese remainder reduction map associated to projective space of an ideal with a given factorization into ideals whose radicals are pairwise distinct maximal ideals. In Theorem $2$ we prove the surjectivity of the reduction map of the strong approximation type for a ring quotiented by an ideal which satisfies unital set condition. In Theorem $3$ we prove for a dedekind domain, for $k \\geq 2$, the map from $k$-dimensional special linear group to the product of projective spaces of $k-$mutually comaximal ideals associating the $k-$rows or $k-$columns is surjective. Finally this article leads to three interesting questions $1, 2, 3$ mentioned in the introduction section.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-12T09:09:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B25",
      "11D79",
      "11E57",
      "20G35",
      "14N99",
      "14G99"
    ],
    "keywords": [
      "surjectivity",
      "dimensional special linear group",
      "chinese remainder reduction map",
      "satisfies unital set condition",
      "projective space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}