The paper introduces hemicomplemented lattices and D-Stone lattices, revealing key properties and characterizations.
The notion of hemicomplemented lattices is introduced and some of the properties of these algebras are studied. Some characterization theorems of hemicomplemented lattices are derived with the help of minimal prime D-filters, ideals, and congruences. The notion of D-Stone lattices is introduced and then derived a set of equivalent conditions for a hemicomplemented lattice to become a D-Stone lattice. Hemicom-complemented lattices and D-Stone lattices are characterized in topological terms.
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Ananthapatnayakuni et al. (2025) studied this question.
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