Topological Characterization of Hemicomplemented Almost Distributive Lattices (European Journal of Pure and Applied Mathematics, 2025)
The notion of $\LomD$-stone ADLs is introduced, and their core properties are explored. It is shown that every $\LomD$-stone ADL is hemicomplemented but not vice versa. Several equivalent conditions are given for when a hemicomplemented ADL becomes $\LomD$-stone. Topological characterizations are provided via minimal prime $\LomD$-filters and their prime spectra.
Keywords: Almost Distributive Lattice (ADL); hemicomplemented ADL; $\LomD$-filter; $\LomD$-stone ADL; Hausdorff space