R. A. Borzooei and M. Bakhshi
Weak implicative hyper BCK-ideals

In this paper first we define the notion of weak implicative hyper BCK-ideal of a hyper BCK-algebra. Then we state and prove some theorems which determine the relationship among this notion and (weak, commutative, (strong) implicative) hyper BCK-ideals, positive implicative hyper BCK-ideals of type 1,3,...,8 and (strong) positive implicative hyper BCK-ideals. Specially, we prove that if H={0,a,b,c} is a hyper BCK-algebra of order 4, such that a*x={0}, for all x in H-{0} and I is a hyper BCK-ideal and weak implicative hyper BCK-ideal of H, then I is a positive implicative hyper BCK-ideal of type 3.