𝒩 -Prime Spectrum of Stone Almost Distributive Lattices

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.

Keywords

• almost distributive lattice (adl)
• stone adl
• ideal
• filter
• annulet
• 𝒩 -filters
• isomorphism
• compact set
• hausdorff space
• 06d99
• 06d15