Abstract
We determine, for which x∈R* the Kummer extension K(Pn√x) is unramified over K, where K is a local field of char. 0 and res.char. p, ζpn∈K, and R is the valuation ring of K. This builds on techniques of Hasse. Actually, a much more general result concerning cyclic Galois extensions of commutative rings is proved.
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