2011/08/16 by Ferreira, Vitor O., Fornaroli, Érica Z., Sánchez, Javier
#16K40 #16S10 (Primary) #16W60 #FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.1108.3311
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.