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This work aims to introduce the concept of hemicomplemented lattices and explore their properties and characterizations.

June 14, 2026Open Access

Hemi-Complemented Lattices

Key Points

This work aims to introduce the concept of hemicomplemented lattices and explore their properties and characterizations.
Introduced the concept of hemicomplemented lattices.
Utilized minimal prime D-filters, ideals, and congruences for characterizations.
Derived equivalent conditions for hemicomplemented lattices to become D-Stone lattices.
Provided characterization theorems for hemicomplemented lattices.
Established conditions under which a hemicomplemented lattice is a D-Stone lattice.
Linked the structures of hemicomplemented and D-Stone lattices with topological properties.

Abstract

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.

Hemi-Complemented Lattices

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Abstract

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