Well-centered overrings of an integral domain

Details Well-centered overrings of an integral domain Well-centered overrings of an integral domain

2003-06-23

arxiv.org/abs/math/0306322v2

J. of Algebra 272 (2) (2004), 435-455

Mathematics

Commutative Algebra

Example 3.11 was replaced

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Well-centered overrings of an integral domain does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Well-centered overrings of an integral domain, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Well-centered overrings of an integral domain will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-513730