Definition:Associated Prime of Module/Definition 2

Definition
Let $A$ be a commutative ring with unity.

Let $M$ be a module over $A$.

Let $\mathfrak p$ be a prime ideal in $A$.

$\mathfrak p$ is an associated prime of $M$ :
 * $M$ contains a submodule which is isomorphic to the quotient ring $A/\mathfrak p$.