Well-centered overrings of an integral domain
| dc.creator | Heinzer, William | |
| dc.creator | Roitman, Moshe | |
| dc.date | 2003-06-23 | |
| dc.date | 2004-05-10 | |
| dc.date.accessioned | 2026-07-07T04:59:07Z | |
| dc.date.available | 2026-07-07T04:59:07Z | |
| dc.description | Let A be an integral domain with field of fractions K. We investigate the structure of the overrings B of A (contained in K) 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. | |
| dc.description | Example 3.11 was replaced | |
| dc.identifier | https://arxiv.org/abs/math/0306322 | |
| dc.identifier | http://arxiv.org/abs/math/0306322 | |
| dc.identifier | J. of Algebra 272 (2) (2004), 435-455 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67853 | |
| dc.subject | Commutative Algebra | |
| dc.subject | 13A15, 13B30, 13G05 | |
| dc.title | Well-centered overrings of an integral domain | |
| dc.type | text |