Abstract:
Firstly, the concept of involutory ideals is introduced in lattice implication algebras and the set of all involutory ideals being a complete boolean lattice is proved. Secondly, the notion of relative annihilators is also introduced and some of its important properties are studied, the set of all annihilators relative to a fixed point being a complete lattice is provided. Finally, it is obtained that a decomposition theorem of an ideal using relative annihilators and the prime ideals theorem of lattice implication algebras is proved.
