Free fields in skew fields

Details Free fields in skew fields Free fields in skew fields

2008-05-27

arxiv.org/abs/0805.4185v1

Mathematics

Rings and Algebras

16 pages

Scientific paper

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.

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