Remark 1

Tag 06CY, permanent. Cite it as [Bourbaki, Tag 06CY].

Let $(x_i)_{i \in I}$ be a family of elements of M. For each $\nu \in \mathbf{N}^{(I)}$ put

x_\nu = \prod_{i \in I} \gamma_{\nu_i}(x_i).

(\lambda_i) \in \mathbf{A}^{(1)}

and

p \in \mathbf{N}

, then we have by Prop. 3 (ii),

\gamma_p \left( \sum_{i \in I} \lambda_i x_i \right) = \sum_{\nu \in \mathbf{N}^{(I)}, |\nu| = p} \lambda^\nu x_\nu.

(6)

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

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