Relation between hyper $K$-algebras with superlattices and hypersemilattices

Document Type : Original Article


1 Department of Mathematics, Maku Branch, Islamic Azad University, Maku, Iran

2 Department of Mathematics, Payame Noor University, p. o. box. 19395-3697, Tehran, Iran


In this paper, by considering the concepts of hypersemilattice and superlattice, we prove that any commutative and positive implicative hyper $K$-algebra, is a hypersemilattice. Moreover, we prove that any bounded commutative hyper $K$-algebra with some conditions, is a superlattice.