A semigroup S with identity is
termed completely right injective if every right unitary S-system is injective. The
semigroup S is called completely injective if every righl and left unitary S-system
is injective. We prove that S is completely injective if and only if S is a
semigroup with zero, where every right ideal and every left ideal of S is
generated by an idempotent. This condition is equivalent to the statement
that S is an inverse semigroup with zero, whose idempotents are dually
well-ordered.