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

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