Normal Ideals of Pseudo-Complemented Distributive Lattices

Abstract

The notion of normlets and normal ideals are introduced in a pseudo-complemented distributive lattice and then normal ideals are characterized in terms of normlets. Some equivalent conditions are derived for a pseudo-complemented lattice to become a disjunctive lattice. The properties of direct products of normal ideals are studied. A set of equivalent conditions is derived for every prime normal ideal to become a minimal prime ideal in topological terms.