Theorem 1 (Steinitz)

Tag 06S2, permanent. Cite it as [Bourbaki, Tag 06S2].

Algebra, chapter V, § 14. Transcendental extensions

— Every extension E of a field K admits a transcendence basis over K. In other words, every extension of a field K is an algebraic extension of a pure extension of K.

By contrast, an extension is not always a pure extension of an algebraic extension (V, p. 171, Ex. 2).

This theorem is a consequence of the following more precise result:

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

Cited by

Theorem 2, § 14
Theorem 1, § 15
Proposition 10, § 17

Cites

Nothing.