{"title":"Semistar operations on conductive domains","authors":"A. Okabe","doi":"10.5036/MJIU.35.11","DOIUrl":null,"url":null,"abstract":"(S3)E⊆E★ and (E★)★=E★. We shall denote the set of semistar operations (resp. the set of star operations) on D by SStar (D) (resp. Star (D)) as in [5]. The main purpose of this paper is to investigate semistar operations on conducive domains. We also study the number of semistar operations. We shall denote the cardinality of a set X by |X| and the symbol⊂means \"proper inclusion\" . Throughout this paper, D denotes an integral domain with quotient field K and D the integral closure of D. Furthermore we always assume D≠K. Any unexplained terminology is standard, as in [7].","PeriodicalId":18362,"journal":{"name":"Mathematical Journal of Ibaraki University","volume":"12 1","pages":"11-19"},"PeriodicalIF":0.0000,"publicationDate":"2003-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"7","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Journal of Ibaraki University","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5036/MJIU.35.11","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 7
Abstract
(S3)E⊆E★ and (E★)★=E★. We shall denote the set of semistar operations (resp. the set of star operations) on D by SStar (D) (resp. Star (D)) as in [5]. The main purpose of this paper is to investigate semistar operations on conducive domains. We also study the number of semistar operations. We shall denote the cardinality of a set X by |X| and the symbol⊂means "proper inclusion" . Throughout this paper, D denotes an integral domain with quotient field K and D the integral closure of D. Furthermore we always assume D≠K. Any unexplained terminology is standard, as in [7].
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