Corollary 2 (Dedekind's theorem)

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

Let E and L be two extensions of K. The set of K-homomorphisms of E into L is free over L. If E is of finite degree over K, the number of K-homomorphisms of E into L is at most equal to $[E : K]$ .

The last assertion follows from the first, taking account of Formula (2).

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

Cited by

§ 10. Galois extensions
Lemma 2, § 10
Example 4, § 10
Proposition 7, § 10
Theorem 3, § 10

Cites

Nothing.