Bourbaki

Example 1

Tag 0CU0, permanent. Cite it as [Bourbaki, Tag 0CU0].

Commutative Algebra, chapter IX, § 1. Vecteurs de Witt

We have

S0=X0+Y0 S_0 = X_0 + Y_0
S1=X1+Y1−∑i=1p−11p(pi)X0iY0p−i. S_1 = X_1 + Y_1 - \sum_{i=1}^{p-1} \frac{1}{p} \binom{p}{i} X_0^i Y_0^{p-i}.

Moreover, Sn−Xn−YnS_n - X_n - Y_n belongs to the ring Z[X0,...,Xn−1,Y0,...,Yn−1]\mathbf{Z}[X_0, ..., X_{n-1}, Y_0, ..., Y_{n-1}].

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

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Translated with machine help, not yet reviewed by a person.