Let be a normal Noetherian local domain of Krull dimension two. We examine intersections of rank one discrete valuation rings that birationally dominate . We restrict to the class of prime divisors that dominate 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.
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William Heinzer, Bruce Olberding, The ideal theory of intersections of prime divisors dominating a normal Noetherian local domain of dimension two. Rend. Sem. Mat. Univ. Padova 144 (2020), pp. 145–158DOI 10.4171/RSMUP/62