{
  "id": "math/0607418",
  "version": "v2",
  "published": "2006-07-18T11:15:16.000Z",
  "updated": "2007-03-20T13:11:42.000Z",
  "title": "The model completion of the theory of modules over finitely generated commutative algebras",
  "authors": [
    "Moshe Kamensky"
  ],
  "comment": "AMSLaTeX, 13 pages, no figures. Part of author's phd thesis",
  "doi": "10.2178/jsl/1245158083",
  "categories": [
    "math.LO"
  ],
  "abstract": "We find the model completion of the theory modules over $A$, where $A$ is a finitely generated commutative algebra over a field $K$. This is done in a context where the field $K$ and the module are represented by sorts in the theory, so that constructible sets associated with a module can be interpreted in this language. The language is expanded by additional sorts for the Grassmanians of all powers of $K^n$, which are necessary to achieve quantifier elimination. The result turns out to be that the model completion is the theory of a certain class of ``big'' injective modules. In particular, it is shown that the class of injective modules is itself elementary. We also obtain an explicit description of the types in this theory.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-03-20T13:11:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C10",
      "03C60"
    ],
    "keywords": [
      "finitely generated commutative algebra",
      "model completion",
      "achieve quantifier elimination",
      "injective modules",
      "additional sorts"
    ],
    "tags": [
      "dissertation",
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......7418K"
    }
  }
}