{"title":"主域中的S-素理想","authors":"Mohamed Aqalmoun","doi":"10.22342/jims.29.1.1201.93-98","DOIUrl":null,"url":null,"abstract":"Let R be a commutative ring and S be a multiplicative subset of R. The S-prime ideal is a generalization of the concept of prime ideal. In this paper, we completely determine all S-prime and S-maximal idealsof a principal domain. It is shown that the intersection of any descending chain of S-prime ideals in a principal domain is an S-prime ideal, also the S-radical is investigated.","PeriodicalId":42206,"journal":{"name":"Journal of the Indonesian Mathematical Society","volume":" ","pages":""},"PeriodicalIF":0.3000,"publicationDate":"2023-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"S-Prime Ideals in Principal Domain\",\"authors\":\"Mohamed Aqalmoun\",\"doi\":\"10.22342/jims.29.1.1201.93-98\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let R be a commutative ring and S be a multiplicative subset of R. The S-prime ideal is a generalization of the concept of prime ideal. In this paper, we completely determine all S-prime and S-maximal idealsof a principal domain. It is shown that the intersection of any descending chain of S-prime ideals in a principal domain is an S-prime ideal, also the S-radical is investigated.\",\"PeriodicalId\":42206,\"journal\":{\"name\":\"Journal of the Indonesian Mathematical Society\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2023-03-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of the Indonesian Mathematical Society\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.22342/jims.29.1.1201.93-98\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the Indonesian Mathematical Society","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22342/jims.29.1.1201.93-98","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
Let R be a commutative ring and S be a multiplicative subset of R. The S-prime ideal is a generalization of the concept of prime ideal. In this paper, we completely determine all S-prime and S-maximal idealsof a principal domain. It is shown that the intersection of any descending chain of S-prime ideals in a principal domain is an S-prime ideal, also the S-radical is investigated.
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