Geodesic
Derivations of $BE$-Algebras from Hyper $BE$-Algebras
Kragujevac Journal of Mathematics, Tome 42 (2018) no. 3, p. 399 .

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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.
Classification : 03G25, 06F35, 08B30
Keywords: (Hyper $BE$-algebra) dual hyper $K$-algebra, fundamental ($BE$-algebra) dual $BCK$-algebra 
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     author = {M. Hamidi and A. B. Saeid},
     title = {Derivations of $BE${-Algebras} from {Hyper} $BE${-Algebras}},
     journal = {Kragujevac Journal of Mathematics},
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M. Hamidi; A. B. Saeid. Derivations of $BE$-Algebras from Hyper $BE$-Algebras. Kragujevac Journal of Mathematics, Tome 42 (2018) no. 3, p. 399 . http://geodesic.mathdoc.fr/item/KJM_2018_42_3_a6/