Corollary

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

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

If $m$ and $n$ are two positive integers, one has

V_m(A) \times V_n(A) \subset V_{m+n}(A) .

This results from formula (53), since $V_m(A)$ is the image of $V^m : W(A) \to W(A)$ .

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

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