Free fields in Malcev-Neumann series rings
Rings and Algebras
2011-08-17 v1
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.
Keywords
Cite
@article{arxiv.1108.3311,
title = {Free fields in Malcev-Neumann series rings},
author = {Vitor O. Ferreira and Érica Z. Fornaroli and Javier Sánchez},
journal= {arXiv preprint arXiv:1108.3311},
year = {2011}
}
Comments
18 pages