Definition 5

Let $A$ be a ring and $M$ an $A$-module. The set of prime ideals $p$ of $A$ such that $M_p \neq 0$ is called the support of $M$ and is denoted by $\operatorname{Supp}(M)$.

As every maximal ideal of $A$ is prime, it follows immediately from § 3, no. 3, Corollary 2 to Theorem 1, that for $A$-module $M$ to be equal to $0$, it is necessary and sufficient that $\operatorname{Supp}(M) = \varnothing$.