JournalsrsmupVol. 144pp. 145–158

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

  • William Heinzer

    Purdue University, West Lafayette, USA
  • Bruce Olberding

    New Mexico State University, Las Cruces, USA
The ideal theory of intersections of prime divisors dominating a normal Noetherian local domain of dimension two cover
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Abstract

Let RR be a normal Noetherian local domain of Krull dimension two. We examine intersections of rank one discrete valuation rings that birationally dominate RR. We restrict to the class of prime divisors that dominate RR 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.

Cite this article

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. 145–158

DOI 10.4171/RSMUP/62