On separable abelian extensions of rings
Let be a ring with , a finite abelian automorphism group of of order where is cyclic of order . for some integers , , and , and the center of whose automorphism group induced by is isomorphic with . Then an abelian extension is defined as a generalization of cyclic extensions of rings, and is an Azumaya algebra over such that if and only if is Galois over with Galois group (the Kanzaki hypothesis).
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