I'm beginning an introductory course on Galois Theory and we've just started to talk about algebraic closed fields and extensions.
The typical example of algebraically closed fields is $\mathbb{C}$ and the typical non-examples are $\mathbb{R}, \mathbb{Q}$ and arbitrary finite fields.
I'm trying to find some explicit, non-typical example of algebraically closed fields, but it seems like a complicated task. Any ideas?
Best Answer
Another concrete example is given by Puiseux's theorem:
Note:
$K\langle\langle X\rangle\rangle=\displaystyle\bigcup_{n\ge1}K((X^{1/n}))$