{
  "id": "1003.3512",
  "version": "v2",
  "published": "2010-03-18T05:53:56.000Z",
  "updated": "2010-09-07T15:39:58.000Z",
  "title": "Rings of low rank with a standard involution",
  "authors": [
    "John Voight"
  ],
  "comment": "17 pages; minor revisions",
  "categories": [
    "math.NT",
    "math.RA"
  ],
  "abstract": "We consider the problem of classifying (possibly noncommutative) R-algebras of low rank over an arbitrary base ring R. We first classify algebras by their degree, and we relate the class of algebras of degree 2 to algebras with a standard involution. We then investigate a class of exceptional rings of degree 2 which occur in every rank n >= 1 and show that they essentially characterize all algebras of degree 2 and rank 3.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-09-07T15:39:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "low rank",
      "standard involution",
      "first classify algebras",
      "exceptional rings",
      "arbitrary base ring"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1003.3512V"
    }
  }
}