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Die Gruppe der \(p^n\)-primären Zahlen für einen Primteiler \({\mathfrak p}\) von \(p\). (German) Zbl 0016.05204
Let \(p\) be a rational prime, \(m = p^n\), \(F\) be an algebraic number field containing a primitive \(m\)-th root of unity \(\zeta\). Then \(\omega\neq 0\) in \(F\) is called a \(p^n\)-primary quantity of \(F\) if the field \(F\left(\root{m} \of{\omega}\right)\) is unramified over \(F\). The author uses a generalized notion of power of \(\zeta\) and proves that every \(\omega\) is the product of certain explicit generalized powers of \(\zeta\) by the trivial factor \(\alpha^m\), \(\alpha\) any quantity of \(F\). He also uses this power representation to determine the corresponding Artin symbol.

MSC:
11Rxx Algebraic number theory: global fields
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