Duality and Rational Modules in Hopf Algebras over Commutative Rings
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 BlattnerMontgomery duality theorem. Finally, we give sufficient conditions to get the purity of $A^\circ$ in $R^A$.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 November 2000
 arXiv:
 arXiv:math/0011207
 Bibcode:
 2000math.....11207A
 Keywords:

 Mathematics  Rings and Algebras;
 16W30;
 16S40
 EPrint:
 AMSLaTeX with xypic