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.
Rezaei, A.; Saeid, A. B.; and Borzooei, R. A.
Relation between Hilbert Algebras and BE–Algebras,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 8,
2, Article 15.
Available at: https://digitalcommons.pvamu.edu/aam/vol8/iss2/15