正规环和相关环扩张的覆盖集的方程

Pub Date : 2023-06-20 DOI:10.21136/CMJ.2023.0358-22

M. Ben Nasr, Ali Jaballah

{"title":"正规环和相关环扩张的覆盖集的方程","authors":"M. Ben Nasr, Ali Jaballah","doi":"10.21136/CMJ.2023.0358-22","DOIUrl":null,"url":null,"abstract":"We establish several finiteness characterizations and equations for the cardinality and the length of the set of overrings of rings with nontrivial zero divisors and integrally closed in their total ring of fractions. Similar properties are also obtained for related extensions of commutative rings that are not necessarily integral domains. Numerical characterizations are obtained for rings with some finiteness conditions afterwards.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Equations for the set of overrings of normal rings and related ring extensions\",\"authors\":\"M. Ben Nasr, Ali Jaballah\",\"doi\":\"10.21136/CMJ.2023.0358-22\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We establish several finiteness characterizations and equations for the cardinality and the length of the set of overrings of rings with nontrivial zero divisors and integrally closed in their total ring of fractions. Similar properties are also obtained for related extensions of commutative rings that are not necessarily integral domains. Numerical characterizations are obtained for rings with some finiteness conditions afterwards.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2023-06-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.21136/CMJ.2023.0358-22\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.21136/CMJ.2023.0358-22","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

我们建立了具有非平凡零除数的环的覆盖集的基数和长度的几个有限性刻画和方程，并在它们的全分式环中整体闭合。对于不一定是积分域的交换环的相关扩展，也得到了类似的性质。在此基础上，得到了具有一些有限性条件的环的数值刻画。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

Equations for the set of overrings of normal rings and related ring extensions

We establish several finiteness characterizations and equations for the cardinality and the length of the set of overrings of rings with nontrivial zero divisors and integrally closed in their total ring of fractions. Similar properties are also obtained for related extensions of commutative rings that are not necessarily integral domains. Numerical characterizations are obtained for rings with some finiteness conditions afterwards.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助