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.
\(\displaystyle 0 \rightarrow B \otimes_A D \rightarrow C \otimes_A D\)
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.