A STUDY ON BI-INTERIOR HYPERIDEALS IN HYPERSEMIGROUPS

Abstract

The concept of hypersemigroups is a generalization of semigroups with sev-eral real-world applications. The notions of hyperideals play an important role in studying hypersemigroups. This paper introduces the concept of bi-interior hyperideals, a combi-nation of bi-hyperideals and interior hyperideals in hypersemigroups. We examine that bi-interior hyperideals generalize other hyperideals, especially bi-hyperideals and interior hyperideals. The intersection and union of bi-interior hyperideals are discussed. Further-more, we provide the generating sets of bi-interior hyperideals. Finally, we apply the notion of bi-interior hyperideals to classifying regular and intra-regular hypersemigroups.