{
  "id": "0707.1134",
  "version": "v3",
  "published": "2007-07-08T10:14:47.000Z",
  "updated": "2007-11-08T17:25:40.000Z",
  "title": "Linearity Defect and Regularity over a Koszul Algebra",
  "authors": [
    "Kohji Yanagawa"
  ],
  "comment": "13 pages. Several proofs have been simplified, and comments on known results have been revised",
  "categories": [
    "math.AC",
    "math.RA"
  ],
  "abstract": "Let A be a Koszul algebra, and $mod A$ the category of finitely generated graded left A-modules. The \"linearity defect\" ld_A(M) of $M \\in mod A$ is an invariant defined by Herzog and Iyengar. An exterior algebra E is a Koszul algebra which is the Koszul dual S^! of a polynomial ring S. Eisenbud et al. showed that $ld_E(M) < \\infty$ for all $M \\in mod E$. Improving their result, we show the following (and many other facts): (*) If A is a Koszul complete intersection, then $reg_{A^!} (M) < \\infty$ and $ld_{A^!} (M) < \\infty$ for all $M \\in mod A^!$. (**) There is a uniform bound of $ld(J)$, where J is a graded ideal of E.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2007-11-08T17:25:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "koszul algebra",
      "linearity defect",
      "regularity",
      "koszul complete intersection",
      "finitely generated graded left a-modules"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0707.1134Y"
    }
  }
}