Abstract
It is well known that a commutative or cocommutative Hopf algebra is faithfully flat over any Hopf subalgebra. Examples of commutative cocommutative cosemisimple Hopf algebras have been found which are not free as modules over certain Hopf subalgebras. In this paper various sufficient conditions are given for a Hopf algebra to be free over a Hopf subalgebra. It is shown that a pointed Hopf algebra is free over any Hopf subalgebra (as a left or right module).
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