Characterizations of \(\mathcal{Q}\mathcal{C}\)-hyperideals in semihypergroups

Abstract

In this article, we introduce the notion of quasi covered hyperideal (QC-hyperideal) in semihypergroups. The greatest quasi covered hyperideal and the quasi hyperbase of a semihypergroup are studied. We discuss some attributes of these hyperideals, as well as their union and intersection properties and their characterizations in semihypergroups and regular semihypergroups. Finally, we establish a relationship between covered hyperideals, the greatest hyperideal, QC-hyperideals, and the quasi hyperbase with the greatest quasi covered hyperideal.