Free fields in skew fields
Rings and Algebras
2008-05-28 v1
Abstract
Building on the work of K. Chiba (J. Algebra 263 (2003), 75-87), we present sufficient conditions for the completion of a division ring with respect to the metric defined by a discrete valuation function to contain a free field, i.e. the universal field of fractions of a free associative algebra. Several applications to division rings generated by torsion-free nilpotent groups, skew Laurent series and related division rings are discussed.
Keywords
Cite
@article{arxiv.0805.4185,
title = {Free fields in skew fields},
author = {Vitor O. Ferreira and Érica Z. Fornaroli},
journal= {arXiv preprint arXiv:0805.4185},
year = {2008}
}
Comments
16 pages