Corollary 1

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

Algebra, chapter V, § 3. Algebraic extensions

— Let $A$ be an algebra over a field $K$ . For an element $x$ of $A$ to be algebraic over $K$ it is necessary and sufficient that the subalgebra $K[x]$ of $A$ generated by $x$ should be of finite degree over $K$ . In particular, if $A$ is of finite degree over $K$ , every element of $A$ is algebraic over $K$ .

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

Cited by

Proposition 3, § 13
Corollary 3, § 14

Cites

Nothing.