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Abstract
It is shown that the skew field of Malcev–Neumann series of an ordered group frequently contains a free field of countable rank, i.e. the universal field of fractions of a free associative algebra of countable rank. This is an application of a criterion on embeddability of free fields on skew fields which are complete with respect to a valuation function, following K. Chiba. Other applications to skew Laurent series rings are discussed. Finally, embeddability questions on free fields of uncountable rank in Malcev–Neumann series rings are also considered.
ACKNOWLEDGEMENT
The first author is the corresponding author and was partially supported by CNPq, Brazil (Grant 308163/2007-9)
The second author was supported by CNPq, Brazil (Grant 141505/2005-2)
The third author was partially supported by FAPESP, Brazil (Proc. 2009/50886-0), by the DGI and the European Regional Development Fund, jointly, through Project MTM2008-06201-C02-01, and by the Comissionat per Universitats i Recerca of the Generalitat de Catalunya, Project 2009 SGR 1389.
Notes
Communicated by I. Shestakov.