{
  "id": "1606.04685",
  "version": "v1",
  "published": "2016-06-15T09:04:41.000Z",
  "updated": "2016-06-15T09:04:41.000Z",
  "title": "Coherence of the ring of periodic distributions",
  "authors": [
    "Amol Sasane"
  ],
  "comment": "10 pages",
  "categories": [
    "math.FA",
    "math.AC",
    "math.GN",
    "math.RA"
  ],
  "abstract": "It is shown that the ring of periodic distributions is a coherent ring (with the operations of pointwise addition and convolution) by showing that the isomorphic ring $s'$ of the Fourier coefficients (of sequences of at most polynomial growth) with termwise operations is coherent. Moreover, it is shown that the subring $\\ell^\\infty$ of $s'$ of all bounded sequences is coherent too, while the subring $c$ of $\\ell^\\infty$ of all convergent sequences is not coherent. It is also observed that $s'$ is a Hermite ring, but not a projective free ring.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-15T09:04:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46F05",
      "13J99",
      "16S15"
    ],
    "keywords": [
      "periodic distributions",
      "convergent sequences",
      "polynomial growth",
      "fourier coefficients",
      "termwise operations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}