H-module endomorphism rings Original Research Article

We discuss the endomorphism ring extension of a module over an H-comodule algebra. A necessary and sufficient condition for such an endomorphism ring extension to be Hopf Galois is obtained. The (weak) H-stability for Hopf modules is introduced to study the endomorphism ring extension of a Hopf module. Moreover, the stable Clifford theory for graded rings and modules is extended to the Hopf case.