Commutative Algebra with a View Toward Algebraic Geometry
《Commutative Algebra with a View Toward Algebraic Geometry》 · 第 95–96 页 · Chapter 3，Section 3.3
If the intersection is minimal, in the sense that there is no such intersection with fewer terms, then each associated prime of $M/M'$ is equal to $P_i$ for exactly one index $i$. In this case, if $P_i$ is minimal over the annihilator of $M/M'$, then $M_i$ is the $P_i$-primary component of $M'$.