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

G. Griffith Elder

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

Number Theory 2007-05-23 v1

Authors: G. Griffith Elder

Abstract

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.

Keywords

cyclic extensions ambiguous ideals galois structure z[c8]-modules ramification invariants indecomposable modules

Cite

@article{arxiv.math/0602060,
  title  = {The Galois structure of ambiguous ideals in cyclic extensions of degree 8},
  author = {G. Griffith Elder},
  journal= {arXiv preprint arXiv:math/0602060},
  year   = {2007}
}

Comments

This article has appeared in the Lect. Notes Pure Appl. Math. without references. The article is being posted here, with permission, to remedy that problem

Related papers

View all related →