Proposition 3

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

Algebra, chapter V, § 14. Transcendental extensions

— For a family $(x_i)_{i \in I}$ , of elements of an extension E of a field K to be algebraically free over K it is necessary and sufficient that every finite subfamily of $(x_i)_{i \in I}$ should be algebraically free over K.

This proposition follows immediately from Def. 1.

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

Cited by

Remark, § 14
Proposition 4, § 14
Proposition 5, § 14
Theorem 2, § 14

Cites

Def. 1