  It is proved in the paper that a Noetherian residually finite dimensional
Hopf algebra is a flat module over any right Noetherian right coideal
subalgebra. In the case of Hopf subalgebras we get faithful flatness. These
results are obtained by verifying the existence of the classical quotient rings
of those algebras. It is also proved that the antipode of either right or left
Noetherian residually finite dimensional Hopf algebra is bijective. As a
consequence, such a Hopf algebra is right and left Noetherian simultaneously.
