Abstract
Let H be a finite‐dimensional Hopf algebra over a field K, H* the dual Hopf algebra of H, and B a right H*‐Galois and Hirata separable extension of BH. Then B is characterized in terms of the commutator subring VB(BH) of BH in B and the smash product VB(BH)#H. A sufficient condition is also given for B to be an H*‐Galois Azumaya extension of BH.
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