Stone’s topology for pseudocomplemented and bicomplemented lattices

Abstract

In an earlier paper the author has proved the existence of prime ideals and prime dual ideals in a pseudocomplemented lattice (not necessarily distributive). The present paper is devoted to a study of Stone’s topology on the set of prime dual ideals of a pseudocomplemented and a bicomplemented lattice. If $\hat L$ is the quotient lattice arising out of the congruence relation defined by $a \equiv b \Leftrightarrow {a^ \ast } = {b^ \ast }$ in a pseudocomplemented lattice $L$, it is proved that Stone’s space of prime dual ideals of $\hat L$ is homeomorphic to the subspace of maximal dual ideals of $L$.