The Stacks project

Exercise 111.5.2. Find an injection $M_1 \to M_2$ of $A$-modules such that $M_1\otimes N \to M_2 \otimes N$ is not injective in the following cases:

1. $A = k[x, y]$ and $N = (x, y) \subset A$. (Here and below $k$ is a field.)

2. $A = k[x, y]$ and $N = A/(x, y)$.