Proposition 2

Tag 060D, permanent. Cite it as [Bourbaki, Tag 060D].

Let $(E_\lambda)_{\lambda \in L}$ and $(F_\mu)_{\mu \in M}$ be two families of $A$ -algebras. The canonical mapping (II, § 3, no. 7)

\left( \bigoplus_{\lambda \in L} E_\lambda \right) \otimes_A \left( \bigoplus_{\mu \in M} F_\mu \right) \to \bigoplus_{(\lambda, \mu) \in L \times M} (E_\lambda \otimes_A F_\mu)

is an algebra isomorphism.

This follows immediately from II, § 3, no. 7, Proposition 7 and the definition of multiplication on $E \otimes F$ .

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

Cited by

Nothing.