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Zur Arithmetik der zyklischen $$p$$-Körper. (German) Zbl 0016.05205
Let $$k$$ be a perfect field of characteristic $$p$$, $$\mathbf K$$ be an algebraic extension of finite degree over a simple transcendental extension of $$k$$. Then H. Hasse has developed the arithmetic theory of cyclic fields $$\mathbf Z$$ of degree $$p$$ over $$\mathbf K$$ [“Theorie der relativ-zyklischen algebraischen Funktionenkörper usw.”, J. Reine Angew. Math. 172, 37–54 (1934; Zbl 0010.00501)]. The author uses the new vector symbolism of E. Witt and generalizes Hasse’s results to the case of cyclic fields of degree $$p^n$$ over $$\mathbf K$$. He also determines which ramification points are Weierstrass points.

##### MSC:
 11R20 Other abelian and metabelian extensions
cyclic p-fields
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