  A well known result of Lozanovsky states that a Banach lattice is weakly
sequentially complete if and only if it does not contain a copy of $c_{0}$. In
the current paper we extend this result to the class of Banach $C(K)$ modules
of finite multiplicity and, as a special case, to finitely generated Banach
$C(K)$-modules. Moreover, we prove that such a module is weakly sequentially
complete if and only if each cyclic subspace of the module is weakly
sequentially complete.
