In this paper, we ?rst consider the regular and strongly regular relations on ordered semihypergroups in detail. In particular, we introduce the concepts of the hypersemilattice strongly regular relations and complete...In this paper, we ?rst consider the regular and strongly regular relations on ordered semihypergroups in detail. In particular, we introduce the concepts of the hypersemilattice strongly regular relations and complete hypersemilattice strongly regular relations on ordered semihypergroups, and investigate their related properties.Furthermore, the properties of hyper?lters of an ordered semihypergroup are studied,and several related applications are given. Especially, we prove that the equivalence relation N on an ordered semihypergroup S is the least complete hypersemilattice strongly regular relation on S.展开更多
基金The NSF(11801081,11701504) of Chinathe University Natural Science Project(KJ2018A0329) of Anhui Province
文摘In this paper, we ?rst consider the regular and strongly regular relations on ordered semihypergroups in detail. In particular, we introduce the concepts of the hypersemilattice strongly regular relations and complete hypersemilattice strongly regular relations on ordered semihypergroups, and investigate their related properties.Furthermore, the properties of hyper?lters of an ordered semihypergroup are studied,and several related applications are given. Especially, we prove that the equivalence relation N on an ordered semihypergroup S is the least complete hypersemilattice strongly regular relation on S.
