{
  "id": "1904.10911",
  "version": "v1",
  "published": "2019-04-24T16:36:16.000Z",
  "updated": "2019-04-24T16:36:16.000Z",
  "title": "The ring $\\mathrm{M}_{8k+4}(\\mathbb{Z}_2)$ is nil-clean of index four",
  "authors": [
    "Yaroslav Shitov"
  ],
  "comment": "note, 1 page",
  "categories": [
    "math.CO",
    "math.RA"
  ],
  "abstract": "We show that the direct sum of an odd number of matrices $$C=\\left(\\begin{array}{cccc} 0&0&0&1\\\\ 1&0&0&0\\\\ 0&1&0&0\\\\ 0&0&1&1 \\end{array}\\right)$$ cannot be a sum $P+Q$ of matrices over $\\mathbb{F}_2$ satisfying $P^2=P$ and $Q^3=O$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-24T16:36:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "direct sum",
      "odd number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 1,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}