FINITE LATTICE IMPLICATION ALGEBRAS

In this paper, by considering a finite lattice implication algebra L and A ϵ L, the set of all co-atoms of L, we prove that L is equal to the filter generated by A, that is L = [A). We give a correspondence theorem between the non-trivial minimal filters and co-atoms of L. We prove that if A = (a1, a2, ... an) then L= a1) [a2) ... an). Finally, we give a characterization of finite lattice implication algebras. In particular, we show that there exists only one lattice implication algebra of prime order.