{
  "id": "0801.1632",
  "version": "v1",
  "published": "2008-01-10T16:47:20.000Z",
  "updated": "2008-01-10T16:47:20.000Z",
  "title": "Uppers to zero in polynomial rings and Prüfer-like domains",
  "authors": [
    "Gyu Whan Chang",
    "Marco Fontana"
  ],
  "categories": [
    "math.AC",
    "math.AG"
  ],
  "abstract": "Let $D$ be an integral domain and $X$ an indeterminate over $D$. It is well known that (a) $D$ is quasi-Pr\\\"ufer (i.e, its integral closure is a Pr\\\"ufer domain) if and only if each upper to zero $Q$ in $D[X] $ contains a polynomial $g \\in D[X]$ with content $\\co_D(g) = D$; (b) an upper to zero $Q$ in $D[X]$ is a maximal $t$-ideal if and only if $Q$ contains a nonzero polynomial $g \\in D[X]$ with $\\co_D(g)^v = D$. Using these facts, the notions of UM$t$-domain (i.e., an integral domain such that each upper to zero is a maximal $t$-ideal) and quasi-Pr\\\"ufer domain can be naturally extended to the semistar operation setting and studied in a unified frame. In this paper, given a semistar operation $\\star$ in the sense of Okabe-Matsuda, we introduce the $\\star$-quasi-Pr\\\"ufer domains. We give several characterizations of these domains and we investigate their relations with the UM$t$-domains and the Pr\\\"ufer $v$-multiplication domains.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-01-10T16:47:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "13F05",
      "13A15",
      "13G05",
      "13B25"
    ],
    "keywords": [
      "polynomial rings",
      "prüfer-like domains",
      "integral domain",
      "integral closure",
      "multiplication domains"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0801.1632C"
    }
  }
}