Wichayaporn Jantanan, Chinnawat Jumnongphan, Natthawut Jaichot, R. Chinram
{"title":"Semigroups in which the radical of every interior ideal is a subsemigroup","authors":"Wichayaporn Jantanan, Chinnawat Jumnongphan, Natthawut Jaichot, R. Chinram","doi":"10.56415/qrs.v31.05","DOIUrl":null,"url":null,"abstract":"In this paper, we characterize when the radical $\\sqrt{I}$ of every interior ideal $I$ of a semigroup $S$ is a subsemigroup of $S$. Also, the radical of every interior ideal (or right ideal or left ideal or quasi-ideal or ideal or bi-ideal or subsemigroup) of $S$ is an interior ideal (or a right ideal or a left ideal or a quasi-ideal or an ideal or a bi-ideal) of $S$.","PeriodicalId":38681,"journal":{"name":"Quasigroups and Related Systems","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Quasigroups and Related Systems","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.56415/qrs.v31.05","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we characterize when the radical $\sqrt{I}$ of every interior ideal $I$ of a semigroup $S$ is a subsemigroup of $S$. Also, the radical of every interior ideal (or right ideal or left ideal or quasi-ideal or ideal or bi-ideal or subsemigroup) of $S$ is an interior ideal (or a right ideal or a left ideal or a quasi-ideal or an ideal or a bi-ideal) of $S$.