In this paper, we introduce the concept of semihyperring $(R,+,cdot)$ together with a suitable partial order $le$. Moreover, we introduce and study hyperideals in ordered semihyperrings. Simple ordered semihyperrings are defined and its characterizations are obtained. Finally, we study some properties of quasi-simple and $B$-simple ordered semihyperrings.

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 orde...

This paper deals with a class of hyperstructures called ordered n-ary semihypergroups which are studied by means j-hyperideals for all positive integers 1≤j≤n and n≥3. We first introduce the notion (softly) left regularity, right intra-regularity, complete generalized regularity investigate their related properties. Several characterizations them in terms provided. Finally, relationships betwee...

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