Definition:Support of Module

Definition

Let $A$ be a commutative ring with unity.

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

The support $\map \supp M$ of $M$ is the set of prime ideals $P$ of $A$ such that the localization of $M$ at $P$ is nonzero:

$\map \supp M = \set {P \in \Spec A : M_P \ne 0}$

where $\Spec A$ is the spectrum of $A$.