交换代数里的定理也很妙啊

Commutative Algebra by Matsumura, Page 55, (8.G) THEOREM 11.

Let $A$ be a noetherian ring and $M$ an $A$-module. Then one can choose a $\mathfrak{p}$-primary submodule $Q(\mathfrak p)$ for each $\mathfrak p\in \mathrm{Ass}(M)$ in such a way that $(0)=\bigcap\limits_{\mathfrak p\in \mathrm{Ass}(M)}Q(\mathfrak p)$.
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