The ideal theory of intersections of prime divisors dominating a normal Noetherian local domain of dimension two

Abstract

Let $R$ be a normal Noetherian local domain of Krull dimension two. We examine intersections of rank one discrete valuation rings that birationally dominate $R$. We restrict to the class of prime divisors that dominate $R$ and show that if a collection of such prime divisors is taken below a certain ``level,'' then the intersection is an almost Dedekind domain having the property that every nonzero ideal can be represented uniquely as an irredundant intersection of powers of maximal ideals.

This article appears in a special issue of Rend. Sem. Mat. Univ. Padova dedicated to Laszlo Fuchs