Definition 1

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

— If G is of finite index in H, we denote by $\mathrm{Tr}_{H/G}$ the mapping of $M^G$ into $M^H$ defined by

\mathrm{Tr}_{H/G} m = \sum_{x \in H/G} x m .

This mapping is a homomorphism of the A-module $M^G$ into the A-module $M^H$ .

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

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