LI-ideals in lattice implication algebras

We define an LI-ideal of a lattice implication algebra and show that every LI-ideal is a lattice ideal. We give an exampl that a lattice ideal may not be an LI-ideal, and show that every lattice ideal is an LI-ideal in a lattice H implication algebra. we discuss the relationship between filters and LI-ideals, and study how to generate an LI-ideal by a set. We construct the quotient structure by using an LI-ideal, and study the properties of LI-ideals related to implication homomorphisms.

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