Remarque 5

Tag 0DX1, permanent. Cite it as [Bourbaki, Tag 0DX1].

Algebra, chapter X, § 5. Modules d’extensions

Let $P^\circ$ and $Q^\circ$ be two right $A$ -modules. We define $\operatorname{Ext}_A(P,Q)$ by

\operatorname{Ext}_A(P,Q)=H(\operatorname{Homgr}_A(L(P),I(Q)))=H(\operatorname{Homgr}_{A^\circ}(L(P^\circ),I(Q^\circ)))

=\operatorname{Ext}_{A^\circ}(P^\circ,Q^\circ).

All the definitions and propositions of this paragraph therefore apply to right $A$ -modules by considering them as left modules over the ring $A^\circ$ .

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

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