{
  "id": "1407.1362",
  "version": "v2",
  "published": "2014-07-05T05:25:33.000Z",
  "updated": "2014-10-19T10:45:41.000Z",
  "title": "On the endomorphism rings of abelian groups and their Jacobson radical",
  "authors": [
    "V. Bovdi",
    "A. Grishkov",
    "M. Ursul"
  ],
  "comment": "14 pages",
  "categories": [
    "math.GR",
    "math.GN",
    "math.RA"
  ],
  "abstract": "We give a characterization of those abelian groups which are direct sums of cyclic groups and the Jacobson radical of their endomorphism rings are closed. A complete characterization of $p$-groups $A$ for which $(EndA,\\mathcal T_L)$ is locally compact, where $\\mathcal T_L$ is the Liebert topology on $EndA$, is given. We prove that if $A$ is a countable elementary $p$-group then $EndA$ has a non-admissible ring topology. To every functorial topology on $A$ a right bounded ring topology on $EndA$ is attached. By using this topology we construct on $EndA$ a non-metrizable and non-admissibe ring topology on $EndA$ for elementary countable $p$-groups $A$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-05T05:25:33.000Z",
      "abstract": "We give a characterization of abelian groups which are direct sums of cyclic groups with closed Jacobson radical of their endomorphism rings.",
      "comment": "12 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-10-19T10:45:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16W80",
      "16A65",
      "16S50",
      "16N40"
    ],
    "keywords": [
      "abelian groups",
      "endomorphism rings",
      "jacobson radical",
      "direct sums"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.1362B"
    }
  }
}