关键词: lattice implication algebras, M V-algebras, lattice order groups, categorical equivalence

Abstract:  Lattice implication algebras is an algebraic structure which is established by combining lattice and implication algebras．In this paper，the relationship between lattice implication algebras and M V-algebra was discussed，and then proved that both of the categorys of the two algebras are categorical equivalence．Finally，the infinitely distributivity in lattice implication algebras were proved．

Key words: lattice implication algebras, M V-algebras, lattice order groups, categorical equivalence