September 10, 2025Open Access

Topological Characterization of Hemicomplemented Almost Distributive Lattices

Key Points

Every $ ext{LomD}$-stone ADL is hemicomplemented, showing a clear connection between the two concepts.
Equivalent conditions establish when a hemicomplemented ADL becomes $ ext{LomD}$-stone, deepening understanding of their interactions.
Topological characterizations using minimal prime $ ext{LomD}$-filters enhance the framework for analyzing these structures.
This framework highlights new exploring avenues in lattice theory and its applications.

Abstract

The notion of -stone ADLs is introduced, and their core properties are explored. It is shown that every -stone ADL is hemicomplemented but not vice versa. Several equivalent conditions are given for when a hemicomplemented ADL becomes -stone. Topological characterizations are provided via minimal prime -filters and their prime spectra.

Topological Characterization of Hemicomplemented Almost Distributive Lattices

Key Points

Abstract

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