  Lee and Kwon [12] defined an ordered semigroup S to be completely regular if
a 2 (a2Sa2] for every a 2 S. We characterize every completely regular ordered
semigroup as a union of t-simple subsemigroups, and every Clifford ordered
semigroup as a complete semilattice of t-simple subsemigroups. Green's Theorem
for the completely regular ordered semigroups has been established. In an
ordered semigroup S, we call an element e an ordered idempotent if it satisfies
e ? e2. Different characterizations of the regular, completely regular and
Clifford ordered semigroups are done by their ordered idempotents. Thus a
foundation for the completely regular ordered semigroups and Clifford ordered
semigroups has been developed
