Bourbaki

Example

Tag 05V2, permanent. Cite it as [Bourbaki, Tag 05V2].

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

Let B be a basis of V over K. For every subfield K' of K, the vector sub-K'-space of V generated by B admits B as a basis over K' and hence is a K'-structure on V. For example, if K is commutative and V is taken to be the polynomial K-algebra K[X1, ..., X_n], then, for every subfield K' of K, K'[X_1, ..., X_n] is a K'-structure on V.*

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

Cited by

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Cites

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Transcribed from the printed edition, 1998, Springer. Not translated.