{"title":"The complete integral closure of a Prüfer domain is a topological property","authors":"Dario Spirito","doi":"arxiv-2409.11189","DOIUrl":null,"url":null,"abstract":"We show that the prime spectrum of the complete integral closure $D^\\ast$ of\na Pr\\\"ufer domain $D$ is completely determined by the Zariski topology on the\nspectrum $\\mathrm{Spec}(D)$ of $D$.","PeriodicalId":501475,"journal":{"name":"arXiv - MATH - Commutative Algebra","volume":"39 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Commutative Algebra","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.11189","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We show that the prime spectrum of the complete integral closure $D^\ast$ of
a Pr\"ufer domain $D$ is completely determined by the Zariski topology on the
spectrum $\mathrm{Spec}(D)$ of $D$.
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