• SPECIAL CLASSES OF IDEALS AND FILTERS OF PSEUDO-COMPLEMENTED ALMOST DISTRIBUTIVE LATTICES

CH. SANTHI SUNDAR RAJ, M. SANTHI*, K. RAMANUJA RAO

Abstract


In this paper we introduce the concepts of αideal and βfilter 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 αideals and βfilters of a pseudo-complemented ADL form algebraic lattices. Also, we characterize Stone ADLs and Almost Boolean algebras in terms of αideals and βfilters.


Keywords


Almost Distributive Lattice(ADL); weak pseudo-complementation; pseudo-complementation; α−ideal; β−filter; minimal prime ideal; Almost Boolean algebra.

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