Generating properties and integrals for Hopf algebras over rings
by
Alexander Seidel
Heinrich-Heine-Universitaet Duesseldorf

For a Hopf algebra H (projective over the ground ring R) the property ''H is a generator in the category of (right) H-comodules'' is not very well known. It is easy to see, that over a field it is equivalent to H being a co-Frobenius Hopf algebra. In this talk we prove - using local-global techniques - that over any noetherian ring this property makes the antipode of H injective. Under stronger assumptions on the ground ring (R artinian) it is strong enough to make the antipode of H bijective. If R is a QF ring it is even equivalent to H being a co-Frobenius Hopf algebra.

Date received: July 12, 2000