Document Type: Original Manuscript


1 Department of Mathematics-Yazd University-Yazd-Iran

2 Department Of Mathematics-Yazd University-Yazd-Iran

3 Department of Mathematics, Payame Noor University, Tehran, Iran


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)
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.