{"title":"关于有序半群的双理想半群","authors":"SUSMITA MALLICK, KALYAN HANSDA","doi":"10.46793/kgjmat2303.339m","DOIUrl":null,"url":null,"abstract":"The purpose of this paper is to characterize an ordered semigroup S in terms of the properties of the associated semigroup B(S) of all bi-ideals of S. We show that an ordered semigroup S is a Clifford ordered semigroup if and only if B(S) is a semilattice. The semigroup B(S) is a normal band if and only if the ordered semigroup S is both regular and intra regular. For each subvariety V of bands, we characterize the ordered semigroup S such that B(S) ∈ V.","PeriodicalId":44902,"journal":{"name":"Kragujevac Journal of Mathematics","volume":"108 1","pages":"0"},"PeriodicalIF":1.0000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"On the Semigroup of Bi-Ideals of an Ordered Semigroup\",\"authors\":\"SUSMITA MALLICK, KALYAN HANSDA\",\"doi\":\"10.46793/kgjmat2303.339m\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The purpose of this paper is to characterize an ordered semigroup S in terms of the properties of the associated semigroup B(S) of all bi-ideals of S. We show that an ordered semigroup S is a Clifford ordered semigroup if and only if B(S) is a semilattice. The semigroup B(S) is a normal band if and only if the ordered semigroup S is both regular and intra regular. For each subvariety V of bands, we characterize the ordered semigroup S such that B(S) ∈ V.\",\"PeriodicalId\":44902,\"journal\":{\"name\":\"Kragujevac Journal of Mathematics\",\"volume\":\"108 1\",\"pages\":\"0\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Kragujevac Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.46793/kgjmat2303.339m\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Kragujevac Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.46793/kgjmat2303.339m","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
On the Semigroup of Bi-Ideals of an Ordered Semigroup
The purpose of this paper is to characterize an ordered semigroup S in terms of the properties of the associated semigroup B(S) of all bi-ideals of S. We show that an ordered semigroup S is a Clifford ordered semigroup if and only if B(S) is a semilattice. The semigroup B(S) is a normal band if and only if the ordered semigroup S is both regular and intra regular. For each subvariety V of bands, we characterize the ordered semigroup S such that B(S) ∈ V.
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