{"title":"残差函数和除法理想","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":"{\"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}","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}
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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