In this paper, we further study the theory of A-subsets in lattice implication algebras. To begin with, we introduce the propositions of homomorphism image and original image of A-subsets in lattice implication algebras. In addition, the notion of A*-subsets is introduced and some properties of A*-subsets are also investigated in lattice implication algebras. Finally, we introduce the notion of involutory LI-ideals with respect to an LI-ideal A and denote the set of all of them by SA (L). Then SA (L) can be made into a complete Boolean lattice and a lattice implication algebra with respect to the suit operations, respectively.
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