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**pascal4542** Give an example of a ring $\displaystyle A$ and $\displaystyle A$-modules $\displaystyle B, C, D$ such that $\displaystyle 0 \rightarrow B \rightarrow C$ is exact, yet

$\displaystyle 0 \rightarrow B \otimes_A D \rightarrow C \otimes_A D$

is not exact.

I cannot think of an example where this would be true. Initially, I was thinking to use $\displaystyle A=\mathbb{Z}$ and then use ideals from that. However, I do not think that my example actually works. I need some help here. Thanks.