2003/06/30 by William Heinzer, Moshe Roitman
Mathematics · #math.AC #msc:13A15 #msc:13B30 #msc:13G05
published as J. of Algebra 272 (2) (2004), 435-455 · Example 3.11 was replaced
arxiv created 2004/05/10 · arxiv updated 2009/11/30
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.