Corollary 2

Tag 0632, permanent. Cite it as [Bourbaki, Tag 0632].

The graded algebra $\bigwedge(M)$ is alternating ( $§ 4$ , no. 9).

It suffices to apply Proposition 13 of $§ 4$ , no. 9 to $\bigwedge(M)$ , taking as generating system the set $M$ and using Proposition 5.

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

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