Well-centered overrings of an integral domain

William Heinzer, Moshe Roitman

Research output: Contribution to journalArticlepeer-review


Let A be an integral domain with field of fractions K. We investigate the structure of the overrings B ⊆ K of A that are well-centered on A in the sense that each principal ideal of B is generated by an element of A. We consider the relation of well-centeredness to the properties of flatness, localization and sublocalization for B over A. If B = A[b] is a simple extension of A, we prove that B is a localization of A if and only if B is flat and well-centered over A. If the integral closure of A is a Krull domain, in particular, if A is Noetherian, we prove that every finitely generated flat well-centered overring of A is a localization of A. We present examples of (non-finitely generated) flat well-centered overrings of a Dedekind domain that are not localizations.

Original languageEnglish
Pages (from-to)435-455
Number of pages21
JournalJournal of Algebra
Issue number2
StatePublished - 15 Feb 2004


  • Flat extension
  • Localization
  • Overring
  • Sublocalization
  • Well-centered

ASJC Scopus subject areas

  • Algebra and Number Theory


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