Corollary 1

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

If $E'$ is a submodule of $E$ , $E'_{(K)}$ is canonically identified with a vector subspace of $E_{(K)}$ and $(E/E')_{(K)}$ with $E_{(K)}/E'_{(K)}$ .

It suffices to apply Proposition 27 to the exact sequence

0 \to E' \to E \to E/E' \to 0.

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

Cited by

Corollary 2, § 7

Cites

Proposition 27