{"title":"Residual functions and divisorial ideals","authors":"Dario Spirito","doi":"arxiv-2409.11846","DOIUrl":null,"url":null,"abstract":"We define a \\emph{residual function} on a topological space $X$ as a function\n$f:X\\longrightarrow\\mathbb{Z}$ such that $f^{-1}(0)$ contains an open dense\nset, and we use this notion to study the freeness of the group of divisorial\nideals on a Pr\\\"ufer domain.","PeriodicalId":501314,"journal":{"name":"arXiv - MATH - General Topology","volume":"11 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - General Topology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.11846","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 define a \emph{residual function} on a topological space $X$ as a function
$f:X\longrightarrow\mathbb{Z}$ such that $f^{-1}(0)$ contains an open dense
set, and we use this notion to study the freeness of the group of divisorial
ideals on a Pr\"ufer domain.
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