##  [Annihilator](/annihilator) 

  ##  [Annihilator](https://algebra.quantumdictionary.io/annihilator-0) 

  

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- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

Given a ring R and an R-module M, the annihilator of a subset S ⊆ M is the ideal Ann_R(S) = { r in R | r·s = 0 for all s in S }; for a single element m it is Ann_R(m). For the whole module M one gets the annihilator ideal Ann_R(M).