Proposition 22

Tag 05TF, permanent. Cite it as [Bourbaki, Tag 05TF].

Let $K$ be a commutative field, $\rho : K \to A$ an injective central homomorphism and $E, F$ two vector spaces over $K$ . Then the canonical homomorphism

\omega : A \otimes_K \operatorname{Hom}(E, F) \to \operatorname{Hom}_A(E_{(A)}, F_{(A)})

(§ 5, no. 3, formula (17)) is injective; it is bijective if $A$ or $E$ is a finite-dimensional vector space over $K$ .

This is a particular case of § 5, no. 3, Proposition 7.

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

Cited by

Nothing.

Cites

§ 5, no. 3
§ 5, no. 3, Proposition 7