Prime Spectrum of Stone Almost Distributive Lattices

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 ℱ (...

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Bibliographic Details
Published inDiscussiones mathematicae. General algebra and applications Vol. 41; no. 2; pp. 299 - 320
Main Authors Rafi, N., Bandaru, Ravi Kumar, Srujana, M.
Format Journal Article
LanguageEnglish
Published Sciendo 01.11.2021
University of Zielona Góra
Subjects
06D15
06D99
Almost Distributive Lattice (ADL)
annulet
compact set
filter
filters
Hausdorff space
ideal
isomorphism
stone ADL
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Summary: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 ℱ ( ) of all 𝒩 -filters is isomorphic to the class ) of all -extentions of . 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.
ISSN:2084-0373
DOI:10.7151/dmgaa.1370