The algebraic structure of a Hopf algebra over a field was established by A. Borel [I] (see Theoreme 6.1). The theorem asserts that if a Hopf algebra is finitely generated in each dimension and the field is perfect then it is algebraically isomorphic to a tensdr product of monogenic exterior and polynomial algebras (the latter possibly truncated if the characteristic is prime). Under more restrictive assumptions a similar structure theorem is proved in [5] (see Theorem 7.13) in the case where the field is replaced by an integral domain. In this note we shall make use of the latter theorem in the case where the Hopf algebra has a system of divided powers and then apply the result to H-spaces.