IDEALS IN EL-SEMIHYPERGROUPS ASSOCIATED TO ORDERED SEMIGROUPS

Abstract

In this paper, we attempt to investigate the connection between various types of ideals (for examples $(m, n)$-ideal, bi-ideal, interior ideal, quasi ideal, prime ideal and maximal ideal)<br /> of an ordered semigroup $(S,cdot ,leq)$ and the correspond hyperideals of its EL-hyperstructure $(S,*)$ (if exists). Moreover, we construct the class of EL-$Gamma$-semihypergroup associated to a partially ordered $Gamma$-semigroup.