##  [Failure of Krull Intersection](/failure-krull-intersection) 

  ##  [Failure of Krull Intersection](https://algebra.quantumdictionary.io/failure-krull-intersection-0) 

  

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- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A phenomenon where the Krull intersection ∩_{n≥1} I^n of powers of an ideal I in a ring R does not equal the expected minimal set (for instance, it is nonzero when theorems predict it should be zero), indicating failure of separation in the I-adic topology or breakdown of hypotheses of intersection theorems.