Abstract
For a Hopf algebra H and an H-module algebra A module-finite over its center it is proved that there is an equivalence relation on a subset SpecfA of the prime spectrum of A which exactly corresponds to the orbit relation in case of group actions. A linearly compact topologically H-simple H-module algebra LP(A) have been associated with each \(P\in\mathop{\rm Spec}_fA\). When A is noetherian and H-semiprime, it is shown that A has a quasi-Frobenius classical quotient ring.
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