Monogenic Hopf algebras and local Galois module theory

Let K be an unramified extension of Qp, and denote the ring of integers of K by . Let H be an R-Hopf algebra with monogenic dual H*. We realize H* as the kernel of an isogeny of one-dimensional formal groups. This allows us to give a complete list of fields L for which L/K is H K-Hopf Galois and is a free H-module.