CANONICAL NONCLASSICAL HOPF-GALOIS MODULE STRUCTURE OF NONABELIAN GALOIS EXTENSIONS

摘要

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.