Definition 1

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

Algebra, V, p. 20, § 4. Algebraically closed extensions

A field K is said to be algebraically closed if it possesses the (equivalent) properties (AC), (AC'), (AC), (AC).

\* Example 1. — The field C of complex numbers is algebraically closed (Gen. Top., VIII, p. 100). \*

A field K which is relatively algebraically closed in an extension field E of K is not necessarily algebraically closed (in effect every field is relatively algebraically closed in itself, and there exist fields that are not algebraically closed, for example Q or $\mathbf{F}_p$ \* or R *). However:

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

Cited by

Proposition 5, § 1

Cites

Example 1