SOME STRUCTURAL PROPERTIES OF HYPER KS-SEMIGROUPS - Davvaz, Bijan; Vicedo, Ann Leslie O.; Vilela, Jocelyn P. (Italian Journal of Pure and Applied Mathematics, 2014)
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.