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.