Corollary

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

Algebra, chapter II, § 5. Extension of the ring of scalars

The mappings $\rho^*(\phi_E)$ and $\phi_{\rho_*(F)}^*$ are injective and respectively identify $\rho^*(E)$ with a direct factor of $\rho^*(\rho_*(\rho^*(E)))$ and $\rho_*(F)$ with a direct factor of $\rho_*(\rho^*(\rho_*(F)))$ .

This is a consequence of Proposition 5 and § 1, no. 9, Corollary 2 to Proposition 15.

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

Cited by

Nothing.

Cites

§ 1, no. 9, Corollary 2 to Proposition 15
Proposition 5