Associated prime to a module

Definition
Let $$R$$ be a commutative unital ring and $$M$$ be a $$R$$-module. A prime ideal $$P$$ of $$R$$ is said to be associated to $$M$$ if it satisfies the following equivalent conditions:


 * $$P$$ is the annihilator of an element of $$M$$
 * There is an injective homomorphism $$A/P \to M$$ of $$A$$-modules

The set of all primes associated to $$M$$ is denoted as $$Ass_RM$$.