Definition 7

Tag 0618, permanent. Cite it as [Bourbaki, Tag 0618].

A graded A-algebra E of type $\mathbf{Z}$ is called anticommutative if for all non-zero homogeneous elements x, y of E

xy = (-1)^{\deg(x)\deg(y)} yx.

The algebra E is called alternating if it is anticommutative and also $x^2 = 0$ for every homogeneous element $x \in E$ of odd degree.

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

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