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Keywords:
pseudo-complemented distributive lattice; dense element; closed element; $\delta$-ideal; Stone lattice; congruence
pseudo-complemented distributive lattice; dense element; closed element; $\delta$-ideal; Stone lattice; congruence
Summary:
The concept of $\delta$-ideals is introduced in a pseudo-complemented distributive lattice and some properties of these ideals are studied. Stone lattices are characterized in terms of $\delta$-ideals. A set of equivalent conditions is obtained to characterize a Boolean algebra in terms of $\delta$-ideals. Finally, some properties of $\delta$-ideals are studied with respect to homomorphisms and filter congruences.
References:
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