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

PBW--filtration over $\bz$ and compatible bases for $V_\bz(\la)$ in type ${\tt A}_n$ and ${\tt C}_n$