Abstract
We give a description of the group H(R, Z p n Z) of cyclic p n -extensions with normal basis over a connected ring R, assuming that the prime p is a unit in R. This generalizes the well-known isomorphism R ∗ R ∗p n ≅H(R, Z p n Z) of Kummer theory for R a field containing the p n th roots of unity. We also study Z p-extensions.
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