Well-centered overrings of an integral domain

JOURNAL OF ALGEBRA

卷:272

Article

Heinzer, W ; Roitman, M

关键词: flat extension;    localization;    overring;    sublocalization;    well-centered;   

DOI  :  10.1016/S0021-8693(03)00462-9

来源: Elsevier

【 摘 要 】

Let A be an integral domain with field of fractions K. We investigate the structure of the overrings B subset of or equal to 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. (C) 2004 Published by Elsevier Inc.

【 授权许可】

Free