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Boolean filters of distributive lattices

Journal: International Journal of Mathematics and Soft Computing (Vol.3, No. 3)

Publication Date:

Authors : ;

Page : 41-48

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.

Last modified: 2013-08-25 01:35:31