Example 1

Tag 0D5X, permanent. Cite it as [Bourbaki, Tag 0D5X].

Commutative Algebra, chapter X, § 4. Anneaux réguliers

If the ring $A$ is regular, the ring of fractions $S^{-1}A$ is regular for every multiplicative subset $S$ of $A$ : this follows for example from characterization (iii) above.

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

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