The associated hyperringoid to a Krasner hyperring

Abstract

"Ends Lemma" is used to construct a hypergroupoid from a (quasi) partially ordered groupoid. But this lemma does not work well for creating a hyperringoid from a (partially) ordered ringoid. In this paper, we plan to gain that by modifying this lemma, called modified "Ends Lemma". Then we construct a EL 2-hyperring, as a generalization of a "EL-hyperring", by applying on a (partially) ordered Krasner hyperring.