Support of a module

Summary

The support of a module $M$ over a commutative ring $R$ is the set of prime ideals $\mathfrak p$ at which the localization $M_{\mathfrak p}$ is nonzero. It is a subset of the spectrum of $R$, and it tells where on that space the module "lives". For a finitely generated module, it is the closed set of primes containing the annihilator of $M$.