β-Prime Spectrum of Stone Almost Distributive Lattices

Abstract

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 𝒡β (L) of all β-filters is isomorphic to the set of all ideals of 𝒝0(L). A set of equivalent conditions is derived for 𝒝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
• β-filters
• isomorphism
• compact set
• hausdorff space
• 06d99
• 06d15