Given that $B$ is a flat $A$-algebra, why is the following an exact sequence of $B$-modules:
$M'\otimes_A B\rightarrow M\otimes_A B \rightarrow M''\otimes_A B \rightarrow 0$, $M$'s are $A$-modules and exact
So how do we view the individual tensor product as a $B$- module; What exactly is the ring action over $M$'s.
Cheers