n-fold commutative hyper k-ideals

in this paper, we aresupposed to introduce the definitions of n-fold commutative, andimplicative hyper k-ideals. these definitions are thegeneralizations of the definitions of commutative, andimplicative hyper k-ideals, respectively, which have been definedin [12]. then we obtain some related results. in particular wedetermine the relationships between n-fold implicative hyperk-ideal and n-fold commutative hyper k-ideals of a hyperk-algebra of order 3, which satisfy the simple condition. then,generally we study n-fold commutative hyper k-ideals in simplehyper k-algebras.