β-Prime Spectrum of Stone Almost Distributive Lattices

The notion of boosters and -filters in stone Almost Distributive Lattices are introduced and their properties are studied, utilizing boosters to characterize the -filters. It has been derived that every proper -filter is the intersection of all prime -filters containing it, and it has also been prov...

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Bibliographic Details
Published inDiscussiones mathematicae. General algebra and applications Vol. 40; no. 2; pp. 311 - 326
Main Authors Rafi, N., Bandaru, Ravi Kumar
Format Journal Article
LanguageEnglish
Published Sciendo 01.12.2020
University of Zielona Góra
Subjects
06D15
06D99
Almost Distributive Lattice (ADL)
booster
compact set
filter
filters
Hausdorff space
ideal
isomorphism
relatively complemented ADL
stone ADL
β-filters
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Summary:The notion of boosters and -filters in stone Almost Distributive Lattices are introduced and their properties are studied, utilizing boosters to characterize the -filters. It has been derived that every proper -filter is the intersection of all prime -filters containing it, and it has also been proved that the set 𝒡 ( ) of all -filters is isomorphic to the set of all ideals of 𝒝 A set of equivalent conditions is derived for 𝒝 ) to become a relatively complemented Almost Distributive Lattice. Later, some properties of the space of all prime -filters are derived topologically. Finally, necessary and sufficient conditions are derived for the space of all prime -filters to be a Hausdorff space.
ISSN:1509-9415
2084-0373
DOI:10.7151/dmgaa.1339