Noncyclic Division Algebras over Fields of Brauer Dimension One

Eric Brussel

Noncyclic Division Algebras over Fields of Brauer Dimension One

Rings and Algebras 2019-03-22 v1

Authors: Eric Brussel

Abstract

Let $K$ be a complete discretely valued field of rank one, with residue field $\Q_p$ . It is well known that period equals index in $\Br(K)$ . We prove that when $p=2$ there exist noncyclic $K$ -division algebras of every $2$ -power degree divisible by four. Otherwise, every $K$ -division algebra is cyclic.

Keywords

division algebras brauer dimension discretely valued fields cyclic algebras period-index

Cite

@article{arxiv.1903.09063,
  title  = {Noncyclic Division Algebras over Fields of Brauer Dimension One},
  author = {Eric Brussel},
  journal= {arXiv preprint arXiv:1903.09063},
  year   = {2019}
}

Comments

8 pages

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