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Boolean filters of distributive latticesKeywords: Pseudo-complemented distributive lattice , Boolean algebra , Boolean filter , maximal filter , congruence. Abstract: In this paper we introduce the notion of Boolean filters in a pseudo-complemented distributive lattice and characterize the class of all Boolean filters. Further a set of equivalent conditions are derived for a proper filter to become a prime Boolean filter. Also a set of equivalent conditions is derived for a pseudo-complemented distributive lattice to become a Boolean algebra. Finally, a Boolean filter is characterized in terms of congruences.
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