Division Rings with Ranks
Logic
2016-05-16 v1 Rings and Algebras
Abstract
Any superrosy division ring (i.e. a division ring equipped with an abstract notion of rank) is shown to be centrally finite. Furthermore, division rings satisfying a generalized chain condition on definable subgroups are studied. In particular, a division ring of burden n has dimension at most n over its center, and any definable group of definable automorphisms of a field of burden n has size at most n. Additionally, interpretable division rings in o-minimal structures are shown to be algebraically closed, real closed or the quaternions over a real closed field.
Cite
@article{arxiv.1605.04118,
title = {Division Rings with Ranks},
author = {Nadja Hempel and Daniel Palacín},
journal= {arXiv preprint arXiv:1605.04118},
year = {2016}
}