Definition:Support of Module

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

Let $M$ be a unitary $A$-module.

The support $\operatorname{Supp}(M)$ of $M$ is the set of prime ideals $P$ of $A$ such that the localization of $M$ at $P$ is nonzero:
 * $\operatorname{Supp}(M) = \{P\in \operatorname{Spec}(A) : M_P\neq0 \}$

where $\operatorname{Spec}(A)$ is the spectrum of $A$.