Duality and Rational Modules in Hopf Algebras over Commutative Rings
  Let $A$ be an algebra over a commutative ring $R$. If $R$ is noetherian and $A^\circ$ is pure in $R^A$, then the categories of rational left $A$-modules and right $A^\circ$-comodules are isomorphic. In the Hopf algebra case, we can also strengthen the Blattner-Montgomery duality theorem. Finally, we give sufficient conditions to get the purity of $A^\circ$ in $R^A$. 
J. Y. Abuhlail (University of Duesseldorf), J. Gomez-Torrecillas and   F. J. Lobillo (Universidad de Granada)