{
  "id": "1712.07463",
  "version": "v1",
  "published": "2017-12-20T13:14:01.000Z",
  "updated": "2017-12-20T13:14:01.000Z",
  "title": "On the finiteness of the Gorenstein dimension for Artin algebras",
  "authors": [
    "Rene Marczinzik"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "In \\cite{SSZ}, the authors proved that an Artin algebra $A$ with infinite global dimension has an indecomposable module with infinite projective and infinite injective dimension, giving a new characterisation of algebras with finite global dimension. We prove in this article that an Artin algebra $A$ that is not Gorenstein has an indecomposable $A$-module with infinite Gorenstein projective dimension and infinite Gorenstein injective dimension, which gives a new characterisation of algebras with finite Gorenstein dimension. We show that this gives a proper generalisation of the result in \\cite{SSZ} for Artin algebras.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-20T13:14:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "artin algebra",
      "finiteness",
      "finite gorenstein dimension",
      "infinite global dimension",
      "infinite gorenstein projective dimension"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}