  Let $L/K$ be a finite Galois extension of local or global fields in
characteristic $0$ or $p$ with nonabelian Galois group $G$, and let ${\mathfrak
B}$ be a $G$-stable fractional ideal of $L$. We show that ${\mathfrak B}$ is
free over its associated order in $K[G]$ if and only if it is free over its
associated order in the Hopf algebra giving the canonical nonclassical
Hopf-Galois structure on the extension.
