Corollary 5

Tag 0D64, permanent. Cite it as [Bourbaki, Tag 0D64].

Commutative Algebra, chapter X, § 4. Anneaux réguliers

Let $A$ be a regular ring, and $(T_i)_{i \in I}$ a finite family of indeterminates. The polynomial ring $A[(T_i)_{i \in I}]$ and the ring of formal series $A[[T_i]_{i \in I}]$ are regular.

This follows from cor. 4 and cor. 3 b).

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

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