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I read a phrase saying that tensoring $\mathbb{Q}$ over $\mathbb{Z}$ is exact. What does it mean for tensoring to be exact?

share|cite|improve this question – Rasmus Mar 13 '12 at 10:04

Each exact sequence $$ \cdots \to A_1 \to A_2 \to A_3 \to \cdots $$ of $\mathbb Z$-modules is mapped to an exact sequence $$ \cdots \to A_1 \otimes_{\mathbb Z} \mathbb Q \to A_2 \otimes_{\mathbb Z} \mathbb Q \to A_3 \otimes_{\mathbb Z} \mathbb Q \to \cdots $$

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