{
  "id": "math/0602493",
  "version": "v2",
  "published": "2006-02-22T12:12:30.000Z",
  "updated": "2006-05-27T10:57:17.000Z",
  "title": "The dimension of a variety",
  "authors": [
    "Ewa Graczyńska",
    "Dietmar Schweigert"
  ],
  "comment": "The results of the paper were presented at the workshop AAA71 and CYA21 at B\\c{e}dlewo, Poland on February 11, 2006. the paper is submitted to Discussiones Mathematicae Algebra and Stochastc Methods, special issue",
  "journal": "published in Discussiones Mathematicae, General Algebra and Applications, 27, 2007, pp. 35--47",
  "categories": [
    "math.LO",
    "cs.LO",
    "math.GM"
  ],
  "abstract": "We invent the notion of a {\\it dimension of a variety} $V$ as the cardinality of all its proper {\\it derived} subvarieties (of the same type). The dimensions of varieties of lattices, varieties of regular bands and other general algebraic structures are determined.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-05-27T10:57:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "08B99",
      "08A40"
    ],
    "keywords": [
      "general algebraic structures",
      "regular bands",
      "subvarieties",
      "cardinality"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......2493G"
    }
  }
}