{
  "id": "2408.13425",
  "version": "v1",
  "published": "2024-08-24T01:36:05.000Z",
  "updated": "2024-08-24T01:36:05.000Z",
  "title": "Syzygies of the residue field over Golod rings",
  "authors": [
    "Doan Trung Cuong",
    "Hailong Dao",
    "David Eisenbud",
    "Toshinori Kobayashi",
    "Claudia Polini",
    "Bernd Ulrich"
  ],
  "categories": [
    "math.AC"
  ],
  "abstract": "Let $(R,m,k)$ be a Golod ring. We show a recurrent formula for high syzygies of $k$ interms of previous ones. In the case of embedding dimension at most $2$, we provided complete descriptions of all indecomposable summands of all syzygies of $k$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-24T01:36:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "13C13",
      "13D09",
      "13H10"
    ],
    "keywords": [
      "residue field",
      "golod ring",
      "recurrent formula",
      "high syzygies",
      "complete descriptions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}