Example 3

Tag 0CQ3, permanent. Cite it as [Bourbaki, Tag 0CQ3].

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

Let k be a field of characteristic $p \neq 0$ and let $n$ be a positive integer. The ring of formal series $k[[X_1, ..., X_n]]$ is complete regular local noetherian, of dimension $n$ , and k is a Cohen subring of $k[[X_1, ..., X_n]]$ .

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

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