{
  "id": "1112.0605",
  "version": "v1",
  "published": "2011-12-02T23:11:07.000Z",
  "updated": "2011-12-02T23:11:07.000Z",
  "title": "On some criteria for the balanced projectivity of modules over integral domains",
  "authors": [
    "J. E. Macías-Díaz"
  ],
  "journal": "International Journal of Algebra 5(2), pp. 57--64, 2011",
  "categories": [
    "math.AC",
    "math.GR"
  ],
  "abstract": "Motivated by Hill's criterion of freeness for abelian groups, we investigate conditions under which unions of ascending chains of balanced-projective modules over integral domains are again balanced-projective. Our main result establishes that, in order for a torsion-free module to be balanced-projective, it is sufficient that it be the union of a countable, ascending chain of balanced-projective, pure submodules. The proof reduces to the completely decomposable case, and it hinges on the existence of suitable families of submodules of the links in the chain. A Shelah-Eklof-type result for the balanced projectivity of modules is proved in the way, and a generalization of Auslander's lemma is obtained as a corollary.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-12-02T23:11:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "13C10",
      "13C05",
      "16D40",
      "13F05"
    ],
    "keywords": [
      "integral domains",
      "balanced projectivity",
      "ascending chain",
      "main result establishes",
      "pure submodules"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1112.0605M"
    }
  }
}