{
  "id": "1601.06655",
  "version": "v1",
  "published": "2016-01-25T16:18:04.000Z",
  "updated": "2016-01-25T16:18:04.000Z",
  "title": "Torsion classes generated by silting modules",
  "authors": [
    "Simion Breaz",
    "Jan Žemlička"
  ],
  "comment": "Preliminary version; comments are welcome",
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "We study the classes of modules which are generated by a silting module. In the case of either hereditary or perfect rings it is proved that these are exactly the torsion $\\mathcal{T}$ such that the regular module has a special $\\mathcal{T}$-preenvelope. In particular every torsion enveloping class in $\\textrm{Mod-} R$ are of the form $\\mathrm{Gen}(T)$ for a minimal silting module $T$. For the dual case we obtain for general rings that the covering torsion-free classes of modules are exactly the classes of the form $\\mathrm{Cogen}(T)$, where $T$ is a cosilting module.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-25T16:18:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "torsion classes",
      "covering torsion-free classes",
      "general rings",
      "perfect rings",
      "dual case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160106655B"
    }
  }
}