{
  "id": "2002.00950",
  "version": "v1",
  "published": "2020-02-03T15:52:34.000Z",
  "updated": "2020-02-03T15:52:34.000Z",
  "title": "On the integral domains characterized by a Bezout Property on intersections of principal ideals",
  "authors": [
    "Lorenzo Guerrieri",
    "K. Alan Loper"
  ],
  "comment": "22 pages",
  "categories": [
    "math.AC"
  ],
  "abstract": "In this article we study two classes of integral domains. The first is characterized by having a finite intersection of principal ideals being finitely generated only when it is principal. The second class consists of the integral domains in which a finite intersection of principal ideals is always non-finitely generated except in the case of containment of one of the principal ideals in all the others. We relate these classes to many well-studied classes of integral domains, to star operations and to classical and new ring constructions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-03T15:52:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "13A15",
      "13F15",
      "13A18",
      "13F05",
      "13G05"
    ],
    "keywords": [
      "integral domains",
      "principal ideals",
      "bezout property",
      "finite intersection",
      "second class consists"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}