## § Tensoring with base ring has no effect

If $0 \rightarrow M' \rightarrow M \rightarrow M''$ is an exact sequence of $A$ modules, then so is $0 \rightarrow A \otimes M' \rightarrow A \otimes M \rightarrow A \otimes M''$. (As an aside, the order is $M', M, M''$ since the middle term $M$ is somehow put together from the other two. So $M$ is the primary. Then by human convention, we choose the single prime on the left and the double prime on the right).