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Relation Between Hilbert Algebras And Be–Algebras, A. Rezaei, A. B. Saeid, R. A. Borzooei

Applications and Applied Mathematics: An International Journal (AAM)

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.