{
  "id": "1607.01095",
  "version": "v1",
  "published": "2016-07-05T02:33:28.000Z",
  "updated": "2016-07-05T02:33:28.000Z",
  "title": "On the generators of the polynomial algebra as a module over the Steenrod algebra",
  "authors": [
    "Dang Vo Phuc",
    "Nguyen Sum"
  ],
  "comment": "9 pages. The detailed proof of Theorem 3.10 of this paper was accepted for publication in Acta Mathematica Vietnamica, available online at arXiv:1502.05569",
  "journal": "Comptes Rendus Mathematique, Volume 353, Issue 11, November 2015, Pages 1035-1040",
  "doi": "10.1016/j.crma.2015.09.002",
  "categories": [
    "math.AT"
  ],
  "abstract": "Let $P_k:= \\mathbb F_2[x_1,x_2,\\ldots,x_k]$ be the polynomial algebra over the prime field of two elements, $\\mathbb F_2$, in $k$ variables $x_1, x_2, \\ldots, x_k$, each of degree 1. We are interested in the Peterson hit problem of finding a minimal set of generators for $P_k$ as a module over the mod-2 Steenrod algebra, $\\mathcal{A}$. In this paper, we study the hit problem in degree $(k-1)(2^d-1)$ with $d$ a positive integer. Our result implies the one of Mothebe [4,5].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-05T02:33:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55S10",
      "55S05",
      "55T15"
    ],
    "keywords": [
      "polynomial algebra",
      "steenrod algebra",
      "generators",
      "peterson hit problem",
      "prime field"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}