Example 4

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

Commutative Algebra, chapter VIII, § 5. Anneaux locaux réguliers

Let $k$ be a complete non-discrete valued field. The ring of formal power series in $n$ variables which converge in a neighbourhood of 0 in $k^n$ is a regular local noetherian ring of dimension $n$ (§ 3, No. 4, Remark 2).

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

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