What is the algebraic closure of the field of rational functions over $\mathbb{Q}$ in variable $t$? Is it true that $\overline{\mathbb{Q}(t)}=\overline{\mathbb{Q}}(t)$?
2026-04-04 17:09:38.1775322578
Algebraic closure of $\mathbb{Q}(t)$
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We definitely have that $\overline{\Bbb Q}(t)\subseteq \overline{\Bbb Q(t)}$, but the other inclusion is not true. For example, in $\overline{\Bbb Q}(t)$, there is no solution to the equation $X^2-t=0$.