##  [Radical Closure](/radical-closure) 

  ##  [Radical Closure](https://algebra.quantumdictionary.io/radical-closure-0) 

  

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- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The operation that assigns to a substructure (typically an ideal) the set of elements whose some power lies in the substructure; for an ideal I, its radical rad(I) = {x | x^n ∈ I for some n ≥ 1}, producing a radical-closed object (an ideal equal to its own radical).