English

Non-existence and splitting theorems for normal integral bases

Number Theory 2009-02-26 v2

Abstract

We establish new conditions that prevent the existence of (weak) normal integral bases in tame Galois extensions of number fields. This leads to the following result: under appropriate technical hypotheses, the existence of a normal integral basis in the upper layer of an abelian tower Q \subset K \subset L forces the tower to be split in a very strong sense.

Keywords

Cite

@article{arxiv.0801.2272,
  title  = {Non-existence and splitting theorems for normal integral bases},
  author = {Cornelius Greither and Henri Johnston},
  journal= {arXiv preprint arXiv:0801.2272},
  year   = {2009}
}

Comments

17 pages, 4 figures, uses xypic, minor revisions following referee's report. To appear in Annales de L'Institut Fourier

R2 v1 2026-06-21T10:03:03.197Z