## Abstract

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 language | English |
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Pages (from-to) | 435-455 |

Number of pages | 21 |

Journal | Journal of Algebra |

Volume | 272 |

Issue number | 2 |

DOIs | |

State | Published - 15 Feb 2004 |

## Keywords

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

## ASJC Scopus subject areas

- Algebra and Number Theory