Valuation bases for generalized algebraic series fields
Commutative Algebra
2013-04-02 v1 Logic
Abstract
We investigate valued fields which admit a valuation basis. Given a countable ordered abelian group G and a real closed, or algebraically closed field F, we give a sufficient condition for a valued subfield of the field of generalized power series F((G)) to admit a K-valuation basis. We show that the field of rational functions F(G) and the field F(G) of power series in F((G)) algebraic over F(G) satisfy this condition. It follows that for archimedean F and divisible G the real closed field F(G) admits a restricted exponential function.
Keywords
Cite
@article{arxiv.0712.4037,
title = {Valuation bases for generalized algebraic series fields},
author = {Franz-Viktor Kuhlmann and Salma Kuhlmann and Jonathan W. Lee},
journal= {arXiv preprint arXiv:0712.4037},
year = {2013}
}