Abstract
Let L/K be a finite Galois extension of local or global fields in any characteristic with nonabelian Galois group G, and let 𝔅 be an ambiguous ideal of L. We show that 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.
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