Implicative hyper $K$-algebras

summary: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