SOME STRUCTURAL PROPERTIES OF HYPER KS-SEMIGROUPS

Abstract

This study introduces a new class of algebra related to hyper BCK-algebras and semihypergroups, called hyper KS-semigroups.  It presents some characterizations of a hyper KS-semigroup with respect to its hyper subKS-semigroups, hyper KS-ideals, and reflexive hyper KS-ideals and their relationships.  A quotient structure is constructed from a hyper KS-semigroup via a reflexive hyper KS-ideal and some properties are established.  This paper also shows some properties of hyper KS-semigroups homomorphism and specifically, the three isomorphism theorems for hyper KS-semigroups are proved.  Moreover, this paper shows that the hyper product of any nonempty finite family of hyper KS-semigroups is also a hyper KS-semigroup and investigates some related properties.