What question did this study set out to answer?

The aim is to define K-filters in distributive lattices and to explore conditions under which certain filters become K-filters.

June 14, 2026Open Access

K-Filters of Distributive Lattices

Key Points

The aim is to define K-filters in distributive lattices and to explore conditions under which certain filters become K-filters.
Introduction of K-filters in distributive lattices.
Derivation of necessary and sufficient conditions for π-filters and D-filters to become K-filters.
Characterization of quasi-complemented lattices using K-filters.
Necessary and sufficient conditions for every π-filter of a distributive lattice to be a K-filter are established.
Equivalent conditions for D-filters to be K-filters in distributive lattices are derived.
Quasi-complemented lattices are characterized through the lens of K-filters.

Abstract

The concept of K-filters is introduced in distributive lattices and studied some properties of these classes of filters. Some necessary and sufficient conditions are derived for every π-filter of a distributive lattice to become a K-filter. Some equivalent conditions are derived for every D-filter of a distributive lattice to become a K-filter. Quasi-complemented lattices are characterized with the help of K-filters.

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