Corollary

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

Let $\lambda \in k$ . If $\lambda$ annihilates $M$ or $N$ , it annihilates $\mathrm{Tor}^A(M, N)$ .

Indeed, $\lambda . 1_{\mathrm{Tor}(M, N)} = \mathrm{Tor}(\lambda . 1_M, 1_N) = \mathrm{Tor}(1_M, \lambda . 1_N)$ .

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

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