The Goldie Theorem for H-semiprime algebras

The main result states that, under certain assumptions about a Hopf algebra H, every H-semiprime right Noetherian H-module algebra has a quasi-Frobenius classical right quotient ring. Another question treated in the paper is concerned with the extension of H-module structures to quotient rings. These results have an application to the semiprimeness problem for smash product algebras A#H.