Consistent Ideals of Pseudo-Complemented Lattices
Asia Pacific Journal of Mathematics · 2024
The notions of consistent ideals, fully consistent F ∇ -ideals, and closed ideals in a pseudocomplemented distributive lattice are introduced, and their characterization theorems are obtained.We also derived a set of equivalent conditions for every ideal of a pseudo-complemented distributive lattice to make it a consistent ideal.The concept of ornate prime F ∇ -ideal is introduced, and established equivalent conditions for every maximal F ∇ -ideal of a pseudo-complemented distributive lattice to make it an ornate prime F ∇ -ideal.