On Quasi-Hyperideals in Semihypergroups

Abstract

In this article, we introduce the notion of quasi-hyperideal in semihypergroups, and moreover, we introduce the notions of an (m, n)-quasi-hyper-ideal, n-right hyperideal, and m-left hyperideal in semihypergroups, and relations between them are studied. We obtain different characterizations concerning different properties of (m, n)-quasi-hyperideals, minimal (m, n)-quasi-hyperideals, minimal m-left hyperideals, and minimal n-right hyperideals, and relations between them are investigated. Also, some intersection properties and characterizations of (m, n)-quasi-hyperideals of semihyperideals and regular semihyperideals have been studied. In the sequel, m-left simple, n-right simple, and (m, n)-quasi-simple semihypergroups are defined, and some properties of them are investigated.