The support $\Supp(M)$ of a module $M$ over a ring $R$ is the set of all prime ideals $\p \subset R$ such that the localization $M_\p$ is nonzero.

The maximal support $\Supp_m(M)$ of a module $M$ over a ring $R$ is the set of all maximal ideals $\m \subset R$ such that $M_\m$ is nonzero.