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Timeline for Completions of $K(x)$

Current License: CC BY-SA 3.0

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May 2, 2017 at 8:23 comment added KConrad Here is an example to think about: completing $\mathbf Q(x)$ at $|\cdot|_{x^2+1}$ will be $\mathbf Q(i)((\pi))$ where $\pi = x^2+1$. This is analogous to completing a number field at a prime ideal with residue field degree greater than $1$. Completing $K(x)$ at $x-c$ gives you $K((x-c))$, so not interesting for your purposes.
May 2, 2017 at 5:40 history edited YCor
edited tags
May 2, 2017 at 0:33 history edited Todd Trimble
completeness tag removed per meta discussion
Nov 22, 2016 at 14:00 history edited David Handelman CC BY-SA 3.0
*different* is followed by *from*, not *than* (despite its use in UK); syntax, ...
Nov 22, 2016 at 13:35 history asked Chilote CC BY-SA 3.0