The L-ordered L-semihypergroups

Abstract

This study pursues an investigation on L-semihypergroups equipped with an L-order. First, the concept of L-ordered L-semihypergroups is introduced by L-posets and L-semihypergroups, and some related results are obtained. Then, prime, weakly prime, and semiprime L-hyperideals of L-ordered L-semihypergroups are studied. Moreover, the relationships among the three types of L-hyperideals are established. Finally, the intra-regular L-ordered L-semihypergroups are characterized in terms of these L-hyperideals. The results of the study show that some well-known results on ordered semihypergroups also hold in the case of L-ordered L-semihypergroups.

Keywords

• l-ordered l-semihypergroup
• l-hyperideal
• prime l-hyperideal
• semiprime l-hyperideal
• weakly prime l-hyperideal
• 06f99
• 20n20
• 20n99