Duality and Rational Modules in Hopf Algebras over Commutative Rings

J. Y. Abuhlail, J. Gomez-Torrecillas, F. J. Lobillo

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 $A^{\circ }$-comodul…