Suppose $M$ is a finitely generated $\mathbb{Z}$-module. I am interested in classifying the associated primes of $M$.
I know that $M$ is an $\mathbb{Z}$-module, it is an abelian group. So I think I can make use of the structure theorem for finitely generated abelian groups. But I am stuck on how to use it to classify the associated primes of $M$.
Any hint/help will be appreciated. Thanks.