Example 4

Tag 0CQ4, permanent. Cite it as [Bourbaki, Tag 0CQ4].

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

Let V be a complete discrete valuation ring and let $n$ be a positive integer. The ring of formal series $V_n = V[[X_1, ..., X_n]]$ is complete regular local noetherian, of dimension $n + 1$ , and V is a Cohen subring of $V_n$ .

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

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