{"title":"𝒩 -Prime Spectrum of Stone Almost Distributive Lattices","authors":"N. Rafi, R. Bandaru, M. Srujana","doi":"10.7151/dmgaa.1370","DOIUrl":null,"url":null,"abstract":"Abstract Introduced the notions of annulets and 𝒩 -filters in stone Almost Distributive Lattices and investigated their properties. Utilized annulets to characterize the 𝒩 -filters. Derived that every proper 𝒩 -filter is the intersection of all 𝒩 -prime filters containing it and also proved that the set ℱ𝒩 (L) of all 𝒩 -filters is isomorphic to the class ConE(L) of all G-extentions of L. Given some topological properties of the space of all 𝒩 -prime filters. Derived a necessary and sufficient condition for the space of all 𝒩 -prime filters to be a Hausdorff space.","PeriodicalId":36816,"journal":{"name":"Discussiones Mathematicae - General Algebra and Applications","volume":"41 1","pages":"299 - 320"},"PeriodicalIF":0.0000,"publicationDate":"2021-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discussiones Mathematicae - General Algebra and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.7151/dmgaa.1370","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 1
Abstract
Abstract Introduced the notions of annulets and 𝒩 -filters in stone Almost Distributive Lattices and investigated their properties. Utilized annulets to characterize the 𝒩 -filters. Derived that every proper 𝒩 -filter is the intersection of all 𝒩 -prime filters containing it and also proved that the set ℱ𝒩 (L) of all 𝒩 -filters is isomorphic to the class ConE(L) of all G-extentions of L. Given some topological properties of the space of all 𝒩 -prime filters. Derived a necessary and sufficient condition for the space of all 𝒩 -prime filters to be a Hausdorff space.
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