Relation between Hilbert Algebras and BE--Algebras.

Hilbert algebras are introduced for investigations in intuitionistic and other non - classical logics and BE-algebra is a generalization of dual BCK-algebra. In this paper, we investigate the relationship between Hilbert algebras and BE-algebras. In fact, we show that a commutative implicative BE-algebra is equivalent to the commutative self distributive BE-algebra, therefore Hilbert algebras and commutative self distributive BE-algebras are equivalent. [ABSTRACT FROM AUTHOR]