Geodesic
β-Prime Spectrum of Stone Almost Distributive Lattices
Discussiones Mathematicae. General Algebra and Applications, Tome 40 (2020) no. 2, pp. 311-326

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The notion of boosters and β-filters in stone Almost Distributive Lattices are introduced and their properties are studied, utilizing boosters to characterize the β-filters. It has been derived that every proper β-filter is the intersection of all prime β-filters containing it, and it has also been proved that the set ℱ_β(L) of all β-filters is isomorphic to the set of all ideals of ℬ_0(L). A set of equivalent conditions is derived for ℬ_0(L) to become a relatively complemented Almost Distributive Lattice. Later, some properties of the space of all prime β-filters are derived topologically. Finally, necessary and sufficient conditions are derived for the space of all prime β-filters to be a Hausdorff space.
Keywords: Almost Distributive Lattice (ADL), stone ADL, relatively complemented ADL, ideal, filter, booster, isomorphism, compact set, Hausdorff space, β-filters 
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     author = {Rafi, N. and Bandaru, Ravi Kumar},
     title = {\ensuremath{\beta}-Prime {Spectrum} of {Stone} {Almost} {Distributive} {Lattices}},
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Rafi, N.; Bandaru, Ravi Kumar. β-Prime Spectrum of Stone Almost Distributive Lattices. Discussiones Mathematicae. General Algebra and Applications, Tome 40 (2020) no. 2, pp. 311-326. http://geodesic.mathdoc.fr/item/DMGAA_2020_40_2_a13/