Semihypergroups associated with ternary relations

Abstract

Davvaz and Leoreanu-Fotea (Commun Algebra 38(10):3621–3636, 2010) studied binary relations on ternary semihypergroups. A ternary relation or triadic relation is a relation in which the number of places in the relation is three. Now, in this paper, instead of binary relations we consider ternary relations and instead of ternary semihypergroups we consider ordinary semihypergroups. Then, we study ternary relations on semihypergroups. In particular, we discuss some properties of compatible ternary relations on them.