Corollary 1

Tag 0E0S, permanent. Cite it as [Bourbaki, Tag 0E0S].

Let $(M_i)_{i \in E}$ be a family of $A$ -modules. We have

\mathrm{dp}_A \left( \bigoplus_{i \in E} M_i \right) = \sup_{i \in E} \mathrm{dp}_A(M_i) .

This follows from the equivalence of conditions (i) and (iii) of Proposition 1 and Proposition 7 of X, p. 89.

In the following statement, we agree that $\pm \infty + 1 = \pm \infty - 1 = \pm \infty$ .

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

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