{"title":"A Class of Congruencies on Distributive Semilattice","authors":"Tolesa Dekeba Bekele, Tesfu Reta","doi":"10.33975/riuq.vol34n1.525","DOIUrl":null,"url":null,"abstract":"In this paper we, contribute the notation of natural epimorphism of a semilattice on the quotient semilattice and subsemilattice. If S is distributive semilattice and F is a filter of S, then we demonstrate that θF is the smallest congruence on S containing F in a single equivalence class and that S/θF is distributive. In addition, the author proved that map FθF is an isomorphism from the lattice of F0(S) all non-empty filters of S into a permutable sublattice of the lattice C(S) of all congruencies on S.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.33975/riuq.vol34n1.525","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper we, contribute the notation of natural epimorphism of a semilattice on the quotient semilattice and subsemilattice. If S is distributive semilattice and F is a filter of S, then we demonstrate that θF is the smallest congruence on S containing F in a single equivalence class and that S/θF is distributive. In addition, the author proved that map FθF is an isomorphism from the lattice of F0(S) all non-empty filters of S into a permutable sublattice of the lattice C(S) of all congruencies on S.
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