{
  "id": "1801.07191",
  "version": "v1",
  "published": "2018-01-22T16:53:33.000Z",
  "updated": "2018-01-22T16:53:33.000Z",
  "title": "Vector lattice covers of ideals and bands in pre-Riesz spaces",
  "authors": [
    "Anke Kalauch",
    "Helena Malinowski"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "Pre-Riesz spaces are ordered vector spaces which can be order densely embedded into vector lattices, their so-called vector lattice covers. Given a vector lattice cover $Y$ for a pre-Riesz space $X$, we address the question how to find vector lattice covers for subspaces of $X$, such as ideals and bands. We provide conditions such that for a directed ideal $I$ in $X$ its smallest extension ideal in $Y$ is a vector lattice cover. We show a criterion for bands in $X$ and their extension bands in $Y$ as well. Moreover, we state properties of ideals and bands in $X$ which are generated by sets, and of their extensions in $Y$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-22T16:53:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46A40",
      "06F20"
    ],
    "keywords": [
      "vector lattice cover",
      "pre-riesz space",
      "smallest extension ideal",
      "ordered vector spaces",
      "extension bands"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}