Definition 1

Tag 0CU7, permanent. Cite it as [Bourbaki, Tag 0CU7].

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

Let $A$ be a ring. The ring $W(A)$ is called the ring of Witt vectors with coefficients in $A$ .

For $a$ in $W(A)$ and $n$ in $\mathbf{N}$ , the element $\Phi_n(a) = \Phi_n(a_0, ..., a_n)$ is sometimes called the ghost component of index $n$ of $a$ .

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

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