Finite lattice implication al-Gebras

Abstract EN

In this paper, by considering a finite lattice implication algebra L and A µ 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 = fa1 ; a2 ; ¢ ¢ ¢ ; ang, 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.