Support of a module M is \text{supp}(M) = \{\mathfrak{p} \in Spec R: M_\mathfrak{p} \neq 0\}
Now, we move on to defining the associated primes of the module. There are finitely many associated points in SpecR.
An associated point is called an embedding point if it is in the closure of some other associated point. This means that if R can be reduced, then there are no embedded points.
We also define that \text{Supp}(M)= \overline{Ass_R M}
We call an element of R a zero-divisor if it vanishes at an associated point. Now we define annihilator ideal Ann_R\ m for m \subset R of a module M Ann_R\ m := \{a \in R: am =0\}.
There is the localization at these associated primes. Given that R is a Noetherian ring and a module M over R, then there is an injection M \rightarrow \Pi_{\mathfrak{p}\in Ass M} M_\mathfrak{p}