The support of a module is closed?
It's well known that under some "weak" hypothesis, such as finitely generated, the support of an A-module is closed in Spec(A). It is true also in the most general case?
Pick a non-closed subset $S$ of $\operatorname{Spec}\mathbb Z$, and let $\displaystyle M=\bigoplus_{\mathfrak p\in S}\:\mathbb Z/{\mathfrak p}$.