{
  "id": "math/0104194",
  "version": "v1",
  "published": "2001-04-19T17:38:05.000Z",
  "updated": "2001-04-19T17:38:05.000Z",
  "title": "On the existence of rigid aleph_1-free abelian groups of cardinality aleph_1",
  "authors": [
    "Rüdiger Göbel",
    "Saharon Shelah"
  ],
  "journal": "Abelian Groups and Modules. Proceedings of the Padova Conference, Padova, Italy, 1994. Editors: A. Facchini and C. Menini. Kluwer, New York, 1995, pp 227--237",
  "categories": [
    "math.LO",
    "math.GR"
  ],
  "abstract": "An abelian group is said to be aleph_1-free if all its countable subgroups are free. Our main result is: If R is a ring with R^+ free and |R|<lambda <= 2^{aleph_0}, then there exists an aleph_1-free abelian group G of cardinality lambda with End(G)=R . A corollary to this theorem is: Indecomposable aleph_1-free abelian groups of cardinality aleph_1 do exist.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-04-19T17:38:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "abelian group",
      "cardinality lambda",
      "main result",
      "countable subgroups"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math......4194G"
    }
  }
}