Strong implicative hyper K-ideals

The study of BCK-algebras was initiated by K. Iséki in 1966 as a generalization of the concept of set-theoretic difference and propositional calculus. The hyperstructure theory (called also multialgebras) is introduced in 1934 by Marty [6] at the 8th congress of Scandinavian Mathematicians. Around the 40’s, several authors worked on hypergroups, especially in France and in the United States, but also in Italy, Russia, Japan, and Iran. Hyperstructures have many applications to several sectors of both pure and applied sciences. Recently in [2] Borzoei et al. and Borzoei and Zahedi [3] constructed the hyper K-algebras, and studied (positive implicative) hyper K-ideals in hyper K-algebras. In [4] Jun and Roh studied strong hyper K-ideals in hyper K-algebras. Also Jun et al. [5] introduced the notion of s-implicative hyper K-ideal of a hyper K-algebra, and investigated related properties. As a continuation of [5], in this paper, we find a condition for a strong hyper K-ideal to be a strong implicative hyper K-ideal. We also consider homomorphic images and inverse images of strong implicative hyper K-ideals.