##  [Support (of a Module)](/support-module) 

  ##  [Support (of a Module)](https://algebra.quantumdictionary.io/support-module-0) 

  

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- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The support of an R-module M is the subset Supp(M) ⊆ Spec(R) consisting of prime ideals p such that the localization M_p is nonzero. Equivalently, it is the set of primes that contain the annihilator of some element of M, and its closure is a topologically closed subset when M is finitely generated.