Corollary

Tag 04E0, permanent. Cite it as [Bourbaki, Tag 04E0].

Commutative Algebra, chapter III, § 2. General results on filtered rings and modules

*Let $A$ be a commutative ring,

A' = A[[X_1, \ldots, X_s]]

the ring of formal power series in $s$ indeterminates over $A$ and $n$ the ideal of $A'$ consisting of the formal power series with no constant term. The ring $A'$ is Hausdorff and complete with the n-adic topology and the polynomial ring $A[X_1, \ldots, X_s]$ is everywhere dense in $A'$ .

It is sufficient to apply what has just been said to the case $m = \{0\}$ .

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

Cited by

Exercise 13, § 2
Proposition 11, § 2
Corollary 2, § 2
Corollary 6, § 2
Remark, § 4

Cites

Nothing.