Duality and Rational Modules in Hopf Algebras over Commutative Rings

Details Duality and Rational Modules in Hopf Algebras over Commutative Rings Duality and Rational Modules in Hopf Algebras over Commutative Rings

2000-11-24

arxiv.org/abs/math/0011207v1

J. Algebra 240, 165-184 (2001)

Mathematics

Rings and Algebras

AMSLaTeX with xypic

Scientific paper

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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