The introduction of regular and π-filters in distributive lattices reveals key conditions for their equivalence.
The concepts of regular filters and π--filters are introduced in distributive lattices. A set of equivalent conditions is given for a D-filter to become a regular filter. For every D-filter, it is proved that there exists a homomorphism whose dense kernel is a regular filter. π--filters are characterized in terms of regular filters and congruences. Some equivalent conditions are given for the space of all prime π-filters to become a Hausdorff space.
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Mukkamala et al. (2023) studied this question.
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