Definition 1

Tag 06VS, permanent. Cite it as [Bourbaki, Tag 06VS].

Let K be a field. An algebra A over K is said to be regular if $L \otimes_K A$ is an integral domain for every extension L of K.

A regular algebra is in particular an integral domain, hence commutative.

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

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