Corollary 1

Tag 0DNL, permanent. Cite it as [Bourbaki, Tag 0DNL].

Algebra, chapter IX, § 9. Algèbres de Clifford

*If $E$ is a free module of dimension $n$ , $C(Q)$ is a free module of dimension $2^n$ ; moreover, if $n > 0$ , $C^+$ and $C^-$ are free modules of dimension $2^{n-1}$ .

This follows at once from the properties of the binomial coefficients.*

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

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