Corollary

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

Algebra, chapter V, § 4. Algebraically closed extensions

— Let $K$ and $K'$ be two fields, $\Omega$ an algebraic closure of $K$ and $\Omega'$ an algebraic closure of $K'$ . For every isomorphism $u$ of $K$ onto $K'$ there exists an isomorphism $v$ of $\Omega$ onto $\Omega'$ extending $u$ .

It is enough to apply Th. 2 to the algebraic closures $\Omega$ and $(\Omega', u)$ of $K$ .

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

Cited by

Nothing.

Cites

Th. 2