We have that any semigroup can be reduced to a ternary semigroup. In this paper, we introduce the concepts of (ordered) filters and (ordered) semilattice congruences of (ordered) ternary semigroups and give some characterizations of (ordered) filters in (ordered) ternary semigroups analogous to the characterizations of ordered left filters in ordered semigroups considered by Lee and Lee [3] and some relationships between the (ordered) filters and the (ordered) semilattice congruences of (ordered) ternary semigroups.

(ordered) ternary semigroup, (ordered) filter, (ordered) semilattice congruence.