Derivations of $BE$-Algebras from Hyper $BE$-Algebras

M. Hamidi, A. B. Saeid

In this paper, we investigate some results in ($BE$-algebras) dual $BCK$-algebras and hyper ($BE$-algebras) dual $K$-algebras. We show that by a set $X$, we can construct a hyper ($BE$-algebra) dual $K$-algebra. By concept of ($BE$-algebras) dual $BCK$-algebras and fundamental relation on hyper ($BE$-algebras) dual $K$-algebras the notion of fundamental ($BE$-algebras) dual $BCK$-algebras is introduced. We prove that any ($BE$-algebra) dual $BCK$-algebra is a fundamental ($BE$-algebra) dual $BCK$-algebra, in practical, any infinite set converts to fundamental ($BE$-algebra) dual $BCK$-algebra of itself.