Median prime ideals of pseudo-complemented distributive lattices

Abstract

. Coherent ideals, strongly coherent ideals, and τ -closed ideals are introduced in pseudo-complemented distributive lattices and their characteri- zation theorems are derived. A set of equivalent conditions is derived for every ideal of a pseudo-complemented distributive lattice to become a coherent ideal. The notion of median prime ideals is introduced and some equivalent conditions are derived for every maximal ideal of a pseudo-complemented distributive lattice to become a median prime ideal which leads to a characterization of Boolean algebras.