The Stacks project

Exercise 109.5.2. 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 $N = A/(x, y)$.

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