Corollary 3 (« universal coefficient formula »)

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

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

Assume $A$ principal and $C$ free. One has for every $A$ -module $N$ and every integer $n$ a split exact sequence (13). Indeed $B(C)$ and $Z(C)$ are free as submodules of the free module $C$ (VII. § 3, cor. 2 to th. 1).

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

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