  It is well-known that a C-monoid is completely integrally closed if and only
if its reduced class semigroup is a group and if this holds, then the C-monoid
is a Krull monoid and the reduced class semigroup coincides with the usual
class group of Krull monoids. We prove that a C-monoid is seminormal if and
only if its reduced class semigroup is a union of groups. Based on this
characterization we establish a criterion (in terms of the class semigroup)
when seminormal C-monoids are half-factorial.
