• SPECIAL CLASSES OF IDEALS AND FILTERS OF PSEUDO-COMPLEMENTED ALMOST DISTRIBUTIVE LATTICES
Abstract
In this paper we introduce the concepts of α−ideal and β−filter of a weakly pseudo-complemented ADL in general and of a pseudo- complemented ADL in particular and discuss certain properties of these. Mainly, we prove that the sets of α−ideals and β−filters of a pseudo-complemented ADL form algebraic lattices. Also, we characterize Stone ADLs and Almost Boolean algebras in terms of α−ideals and β−filters.
Keywords
Almost Distributive Lattice(ADL); weak pseudo-complementation; pseudo-complementation; α−ideal; β−filter; minimal prime ideal; Almost Boolean algebra.
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