{"title":"普吕弗域的完全积分闭包是一种拓扑性质","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":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"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\":null,\"pages\":null},\"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}","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}
The complete integral closure of a Prüfer domain is a topological property
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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