  We study the PBW-filtration on the highest weight representations $V(\la)$ of
the Lie algebras of type ${\tt A}_{n}$ and ${\tt C}_{n}$. This filtration is
induced by the standard degree filtration on $\U(\fn^-)$. In previous papers,
the authors studied the filtration and the associated graded algebras and
modules over the complex numbers. The aim of this paper is to present a proof
of the results which holds over the integers and hence makes the whole
construction available over any field.
