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Keywords:
coherent ideal; strongly coherent ideal; median prime ideal; maximal ideal; Stone lattice; Boolean algebra
coherent ideal; strongly coherent ideal; median prime ideal; maximal ideal; Stone lattice; Boolean algebra
Summary:
Coherent ideals, strongly coherent ideals, and $\tau $-closed ideals are introduced in pseudo-complemented distributive lattices and their characterization 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.
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