  We study the flatness and the projectivity of Hopf algebras, defined over a
Dedekind ring, over their Hopf subalgebras. We give a criterion for the
faithful flatness and use it to show the faithful flatness of an arbitrary flat
Hopf algebra upon its finite normal Hopf subalgebra. For the projectivity of a
projective Hopf algebras we need some finiteness condition in terms of the
module of integral. In particular we show the the module of integral has rank
one.
