Geodesic
Implicative hyper $K$-algebras
Czechoslovak Mathematical Journal, Tome 55 (2005) no. 2, pp. 439-453
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In this note we first define the notions of (weak, strong) implicative hyper $K$-algebras. Then we show by examples that these notions are different. After that we state and prove some theorems which determine the relationship between these notions and (weak) hyper $K$-ideals. Also we obtain some relations between these notions and (weak) implicative hyper $K$-ideals. Finally, we study the implicative hyper $K$-algebras of order 3, in particular we obtain a relationship between the positive implicative hyper $K$-algebras and (weak, strong) implicative hyper $K$-algebras under a simple condition.
In this note we first define the notions of (weak, strong) implicative hyper $K$-algebras. Then we show by examples that these notions are different. After that we state and prove some theorems which determine the relationship between these notions and (weak) hyper $K$-ideals. Also we obtain some relations between these notions and (weak) implicative hyper $K$-ideals. Finally, we study the implicative hyper $K$-algebras of order 3, in particular we obtain a relationship between the positive implicative hyper $K$-algebras and (weak, strong) implicative hyper $K$-algebras under a simple condition.
Classification : 03G25, 06F35
Keywords: hyper $K$-algebra; hyper $K$-ideal; (weak; strong) implicative hyper $K$-algebras; (weak) implicative hyper $K$-ideal 
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Zahedi, M. M.; Saeid, A. Borumand; Borzooei, R. A. Implicative hyper $K$-algebras. Czechoslovak Mathematical Journal, Tome 55 (2005) no. 2, pp. 439-453. http://geodesic.mathdoc.fr/item/CMJ_2005_55_2_a13/

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