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Duality and Rational Modules in Hopf Algebras over Commutative Rings

J. Y. Abuhlail·J. Gomez-Torrecillas·F. J. Lobillo
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Abstract

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 $R^A$.

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BibTeXRIS

J. Y. Abuhlail, J. Gomez-Torrecillas, F. J. Lobillo. 2000-11-24. Duality and Rational Modules in Hopf Algebras over Commutative Rings. https://arxiv.org/abs/math/0011207

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