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

DOI10.4171/RSMUP/62arXiv2306.08569MaRDI QIDQ6440304

Publication date: 14 June 2023

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.

Mathematics Subject Classification ID

Structure, classification theorems for modules and ideals in commutative rings (13C05) Ideals and multiplicative ideal theory in commutative rings (13A15) Local rings and semilocal rings (13H99)

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