ILI-ideals and prime LI-ideals in lattice implication algebras
The notions of ILI-ideals and maximal LI-ideals of lattice implication algebras are introduced, respectively. The properties of ILI-ideals, prime LI-ideals and maximal LI-ideals are investigated. Several characterizations of ILI-ideals and prime LI-ideals are given. The extension theorem of ILI-ideals is obtained. The relations between ILI-ideals and LI-ideals, between ILI-ideals and implication filter, between prime LI-ideals and maximal LI-ideals, between prime LI-ideals and ILI-ideals, between maximal LI-ideals and ILI-ideals, between maximal LI-ideals and LI-ideals, and between prime LI-ideals and LI-ideals are investigated, respectively. Some classes of lattice implication algebras are characterized by their ILI-ideals (respectively prime LI-ideals, maximal LI-ideals).
ili-ideal prime li-ideal lattice implication algebra maximal li-ideal