Dimensional groups and fields
Logic
2019-09-04 v3
Abstract
We shall define a general notion of dimension, and study groups and rings whose interpretable sets carry such a dimensio. In particular, we deduce chain conditions for groups, definability results for fields and domains, and show that pseudofinite groups contain big finite-by-abelian subgroups, and pseudofinite groups of dimension 2 contain big soluble subgroups.
Cite
@article{arxiv.1511.09272,
title = {Dimensional groups and fields},
author = {Frank Olaf Wagner},
journal= {arXiv preprint arXiv:1511.09272},
year = {2019}
}