  We prove three theorems concerning the Hopf-Galois module structure of
fractional ideals in a finite tamely ramified extension of $ p $-adic fields or
number fields which is $ H $-Galois for a commutative Hopf algebra $ H $.
Firstly, we show that if $ L/K $ is a tame Galois extension of $ p $-adic
fields then each fractional ideal of $ L $ is free over its associated order in
$ H $. We also show that this conclusion remains valid if $ L/K $ is merely
almost classically Galois. Finally, we show that if $ L/K $ is an abelian
extension of number fields then every ambiguous fractional ideal of $ L $ is
locally free over its associated order in $ H $.
