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.