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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
##### Keywords:
Number fields, function fields
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