##  [Saturation of Ideals](/index.php/saturation-ideals) 

  ##  [Saturation of Ideals](https://puremath.quantumdictionary.io/saturation-ideals-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

Given an ideal I and an element or ideal J in a ring R, the saturation I : J^∞ = { f ∈ R | ∃ n with J^n f ⊆ I } (commonly I : f^∞ when J = (f)) removes components of V(I) contained in V(J) and produces an ideal whose vanishing set is V(I) minus the part supported inside V(J).