{
  "id": "0912.4412",
  "version": "v3",
  "published": "2009-12-22T14:36:57.000Z",
  "updated": "2012-06-03T06:08:47.000Z",
  "title": "Sum-factor decompositions in rings and arithmetic applications I",
  "authors": [
    "Derong Qiu"
  ],
  "comment": "36 pages; The abstract is slightly changed; the original Remark 3.18 is omitted; the original Theorem 3.16 is written now as Theorem 3.15, and a few new results are added into the present Theorem 3.16, the new Remark 3.17 is added to give some explanation of applications",
  "categories": [
    "math.NT",
    "math.AC"
  ],
  "abstract": "In this paper, by introducing and constructing several new structures about the decomposition phenomenon in algebra, we study the sum-factor collapse property of an arbitrary ring. As an application, we study and analyze several classical problems in additive number theory by this new algebraic and combinatory method. Some further questions are also presented and discussed.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-06-03T06:08:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11P32",
      "05D05",
      "11A41",
      "11T55",
      "13A99",
      "16H05"
    ],
    "keywords": [
      "arithmetic applications",
      "sum-factor decompositions",
      "sum-factor collapse property",
      "decomposition phenomenon",
      "additive number theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0912.4412Q"
    }
  }
}