{
  "id": "math/0311060",
  "version": "v1",
  "published": "2003-11-05T15:11:39.000Z",
  "updated": "2003-11-05T15:11:39.000Z",
  "title": "Star operations and Pullbacks",
  "authors": [
    "Marco Fontana",
    "Mi Hee Park"
  ],
  "comment": "to appear in J. Algebra",
  "categories": [
    "math.AC",
    "math.AG"
  ],
  "abstract": "In this paper we study the star operations on a pullback of integral domains. In particular, we characterize the star operations of a domain arising from a pullback of ``a general type'' by introducing new techniques for ``projecting'' and ``lifting'' star operations under surjective homomorphisms of integral domains. We study the transfer in a pullback (or with respect to a surjective homomorphism) of some relevant classes or distinguished properties of star operations such as $v-, t-, w-, b-, d-,$ finite type, e.a.b., stable, and spectral operations. We apply part of the theory developed here to give a complete positive answer to a problem posed by D. F. Anderson in 1992 concerning the star operations on the ``$D+M$'' constructions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-11-05T15:11:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "13A15",
      "13G05",
      "13C99"
    ],
    "keywords": [
      "star operations",
      "integral domains",
      "surjective homomorphism",
      "complete positive answer",
      "spectral operations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math.....11060F"
    }
  }
}