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OALib Journal期刊
ISSN: 2333-9721
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Boolean filters of distributive lattices

Keywords: Pseudo-complemented distributive lattice , Boolean algebra , Boolean filter , maximal filter , congruence.

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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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