Corollary 2

Tag 05V6, permanent. Cite it as [Bourbaki, Tag 05V6].

Algebra, chapter II, § 8. Restriction of the field ofscalars in vector spaces

Every basis of $V$ over $\mathbf{K}$ which is rational over $\mathbf{K}'$ is a basis of $V'$ over $\mathbf{K}'$ .

If $W'$ is the vector sub- $\mathbf{K}'$ -space of $V'$ generated by $B$ , then $W'.\mathbf{K} = V = V'.\mathbf{K}$ , whence $V' = W'$ by virtue of Proposition 2.

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

Cited by

Nothing.

Cites

Proposition 2