TY - JOUR
TI - Green's Relations for Hypergroupoids
PY - 2018/07/31
Y2 - 2024/05/27
JF - European Journal of Pure and Applied Mathematics
JA - Eur. J. Pure Appl. Math.
VL - 11
IS - 3
LA - en
DO - 10.29020/nybg.ejpam.v11i3.3306
UR - https://doi.org/10.29020/nybg.ejpam.v11i3.3306
SP - 598-611
AB - We give some information concerning the Green's relations $\cal R$ and $\cal L$ in hypergroupoids extending the concepts of right (left) consistent or intra-consistent groupoids in case of hypergroupoids. We prove, for example, that if an hypergroupoid $H$ is right (left) consistent or intra-consistent, then the Green's relations $\cal R$ and $\cal L$ are equivalence relations on $H$ and give some conditions under which in consistent commutative hypergroupoids the relation $\cal R$ (= $\cal L$) is a semilattice congruence. A commutative hypergroupoid is right consistent if and only if it is left consistent and if an hypergroupoid is commutative and right (left) consistent, then it is intra-consistent. A characterization of right (left) consistent (or intra-consistent) right (left) simple hypergroupoids has been also given. Illustrative examples are given.
ER -