Exercise 111.10.1. Compute the set of associated primes for each of the following modules.

$R = k[x, y]$ and $M = R/(xy(x + y))$,

$R = \mathbf{Z}[x]$ and $M = R/(300x + 75)$, and

$R = k[x, y, z]$ and $M = R/(x^3, x^2y, xz)$.

Here as usual $k$ is a field.

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