Structure of H-semiprime artinian algebras

Let H be a Hopf algebra over a field. It is proved that every H-semiprime right artinian left H-module algebra A is quasi-Frobenius and H-semisimple. If H grows slower than exponentially, then all H-equivariant A-modules are shown to be A-projective. With the additional assumption that H is cosemisimple it is proved that the Jacobson radical of any right artinian left H-module algebra is stable under the action of H. © 2010 Springer Science+Business Media B.V