LI-ideals lattice and its prime elements characterizations in a lattice implication algebra
Chunhu Liu · 2014
The concept of LI-ideals in lattice implication algebras L was further studied by using the principle and method of lattice theory.Firstly,the lattice operations ■ and■,implication operation■ and pseudo-complement operation■ are defined on the set ф_(LI/(L) which contains all LI-ideals in L,and(ф_(LI)(L),■,■,■,■,{O},L) is proved to form a complete Heyting algebra.Secondly,some necessary and sufficient conditions of(ф_(LI)(L),■,■,■,■,■,{O},L) becoming a Boolean algebra are given by using properties of operation■.Finally,some equivalent characterizations of prime elements in lattice(ф_(LI)(L),■,■,■,{O},L) are obtained by means of prime LI-ideals in L.