  Let $M$ be a complete nonsingular fine moduli space of modules over an
algebra $S$. A set of conditions is given for the Chow ring of $M$ to be
generated by the Chern classes of certain universal bundles occurring in a
projective resolution of the universal $S$-module on $M$. This result is then
applied to the varieties $G_T$ parametrizing homogeneous ideals of $k[x,y]$ of
Hilbert function $T$, to moduli spaces of representations of quivers, and
finally to moduli spaces of sheaves on ${\Bbb P}^2$, reinterpreting a result of
Ellingsrud and Str\o mme.
