Example 2

Tag 06IO, permanent. Cite it as [Bourbaki, Tag 06IO].

Algebra, V, p. 22, § 4. Algebraically closed extensions

Let K be a field and $\Omega$ an algebraically closed extension of K. If $\overline{K}$ is the relative algebraic closure of K in $\Omega$ , then by V, p. 20, Prop. 2, K is an algebraic closure of K. \* In particular the field of all algebraic numbers (V, p. 20, Ex. 2) is an algebraic closure of the field Q of rational numbers. \*

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

Cited by

Corollary, § 12
Proposition 2, § 4

Cites

V, p. 20
V, p. 20, Prop. 2