Geodesic
Relation Between BE-Algebras and g-Hilbert Algebras
Discussiones Mathematicae. General Algebra and Applications, Tome 38 (2018) no. 1, pp. 33-45

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Hilbert algebras are important tools for certain investigations in algebraic logic since they can be considered as fragments of any propositional logic containing a logical connective implication and the constant 1 which is considered as the logical value “true” and as a generalization of this was defined the notion of g-Hilbert algebra. In this paper, we investigate the relationship between g-Hilbert algebras, gi-algebras, implication gruopoid and BE-algebras. In fact, we show that every g-Hilbert algebra is a self distributive BE-algebras and conversely. We show cannot remove the condition self distributivity. Therefore we show that any self distributive commutative BE-algebras is a gi-algebra and any gi-algebra is strong and transitive if and only if it is a commutative BE-algebra. We prove that the MV -algebra is equivalent to the bounded commutative BE-algebra.
Keywords: (Heyting, implication, (g-)Hilbert) algebra, BE/CI-algebra, dual (S/Q/BCK)-algebra, gi-algebra, implication groupoid, pre-logic, MV - algebra 
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Rezaei, Akbar; Saeid, Arsham Borumand. Relation Between BE-Algebras and g-Hilbert Algebras. Discussiones Mathematicae. General Algebra and Applications, Tome 38 (2018) no. 1, pp. 33-45. http://geodesic.mathdoc.fr/item/DMGAA_2018_38_1_a2/