{
  "id": "1403.7240",
  "version": "v2",
  "published": "2014-03-27T22:52:51.000Z",
  "updated": "2016-06-06T19:12:21.000Z",
  "title": "Conditions for the Yoneda algebra of a local ring to be generated in low degrees",
  "authors": [
    "Justin Hoffmeier",
    "Liana M. Şega"
  ],
  "comment": "Revised version, multiple changes throughout",
  "categories": [
    "math.AC"
  ],
  "abstract": "The powers ${\\mathfrak m}^n$ of the maximal ideal $\\mathfrak m$ of a local Noetherian ring $R$ are known to satisfy certain homological properties for large values of $n$. For example, the homomorphism $R\\to R/{\\mathfrak m}^n$ is Golod for $n\\gg 0$. We study when such properties hold for small values of $n$, and we make connections with the structure of the Yoneda Ext algebra, and more precisely with the property that the Yoneda algebra of $R$ is generated in degrees $1$ and $2$. A complete treatment of these properties is pursued in the case of compressed Gorenstein local rings.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-03-27T22:52:51.000Z",
      "title": "Generalized Koszul properties of commutative local rings",
      "abstract": "We study several properties of commutative local rings that generalize the notion of Koszul algebra. The properties are expressed in terms of the Ext algebra of the ring, or in terms of homological properties of powers of the maximal ideal of the ring. We analyze relationships between these properties and we identify large classes of rings that satisfy them. In particular, we prove that the Ext algebra of a compressed Gorenstein local ring of even socle degree is generated in degrees $1$ and $2$.",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2016-06-06T19:12:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "commutative local rings",
      "generalized koszul properties",
      "ext algebra",
      "socle degree",
      "koszul algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1403.7240H"
    }
  }
}