Corollary 3

Tag 06W5, permanent. Cite it as [Bourbaki, Tag 06W5].

— Let K be an algebraically closed field. If A and B are two K-algebras which are integral domains, then the same is true of $A \otimes_K B$ .

By Cor. 2, A and B are regular K-algebras, and it suffices to apply Prop. 2 (V, p. 141).

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

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