The Galois structure of ambiguous ideals in cyclic extensions of degree 8

Details The Galois structure of ambiguous ideals in cyclic extensions of degree 8 The Galois structure of ambiguous ideals in cyclic extensions of degree 8

2006-02-03

arxiv.org/abs/math/0602060v1

Noncommutative algebra and geometry, Lect. Notes Pure Appl. Math., vol. 243, Chapman & Hall/CRC, Boca Raton, FL, 2006, pp. 63-

Mathematics

Number Theory

This article has appeared in the Lect. Notes Pure Appl. Math. without references. The article is being posted here, with permi

Scientific paper

In cyclic, degree 8 extensions of algebraic number fields $N/K$, ambiguous ideals in N are canonical $\mathbb{Z}[C_8]$-modules. Their $\mathbb{Z}[C_8]$-structure is determined here. It is described in terms of indecomposable modules and determined by ramification invariants. Although infinitely many indecomposable $\mathbb{Z}[C_8]$-modules are available (classification by Yakovlev), only 23 appear.

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