Subfields of algebraically maximal Kaplansky fields
Commutative Algebra
2018-03-22 v1
Abstract
Using the ramification theory of tame and Kaplansky fields, we show that maximal Kaplansky fields contain maximal immediate extensions of each of their subfields. Likewise, algebraically maximal Kaplansky fields contain maximal immediate algebraic extensions of each of their subfields. This study is inspired by problems that appear in henselian valued fields of rank higher than 1 when a Hensel root of a polynomial is approximated by the elements generated by a (transfinite) Newton algorithm.
Keywords
Cite
@article{arxiv.1803.07792,
title = {Subfields of algebraically maximal Kaplansky fields},
author = {Franz-Viktor Kuhlmann},
journal= {arXiv preprint arXiv:1803.07792},
year = {2018}
}