support

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