I read a phrase saying that tensoring $\mathbb{Q}$ over $\mathbb{Z}$ is exact. What does it mean for tensoring to be exact?
What does it mean for tensoring to be exact?
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tensor-products
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0http://en.wikipedia.org/wiki/Flat_module – 2012-03-13
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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 $