TY - JOUR
T1 - Hypersemilattice Strongly Regular Relations on Ordered Semihypergroups
AU - Tang , Jian
AU - Xie , Xiangyun
JO - Communications in Mathematical Research 
VL - 2
SP - 115
EP - 128
PY - 2019
DA - 2019/12
SN - 35
DO - http://doi.org/10.13447/j.1674-5647.2019.02.03
UR - https://global-sci.org/intro/article_detail/cmr/13482.html
KW - ordered semihypergroup, strongly regular relation, hyperfilter
AB - <p style="text-align: justify;">In this paper, we first 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 hyperfilters of an ordered semihypergroup are studied, and several related applications are given. Especially, we prove that the equivalence relation ${\cal N}$ on an ordered semihypergroup $S$ is the least complete hypersemilattice strongly regular relation on $S$.</p>