  Under the assumption that a residually finite dimensional Hopf algebra H has
an Artinian ring of fractions it is proved that H is a flat module over any
right coideal subalgebra satisfying a polynomial identity and is faithfully
flat over any polynomial identity Hopf subalgebra. As a consequence we find a
large class of Hopf algebras which are flat over all coideal subalgebras and
are faithfully flat over all Hopf subalgebras.
