代数极大Kaplansky域的子域
Subfields of algebraically maximal Kaplansky fields
摘要：
利用Tame和Kaplansky场的分歧理论，我们证明了极大Kaplansky场包含其每个子域的极大直接扩张。类似地，代数极大Kaplansky域包含其每个子域的极大立即代数扩张。这项研究的灵感来自于问题，出现在亨塞尔值领域的秩高于1时，一个多项式的亨塞尔根近似由（超限）牛顿算法产生的元素。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
