*-Relations on ternary semigroups

In this paper, we define certain equivalence relations called *-relations on ternary semi-groups and we mention some properties of these relations. We study these relations in respect to Green's relations in ternary semigroups and by bringing some examples, we show that while some propositions are correct for Green's relations, they are not necessarily true for these relations. Then we investigate *-relations in certain ternary semigroups.