##  [Krull–Schmidt Failure](/krull-schmidt-failure) 

  ##  [Krull–Schmidt Failure](https://algebra.quantumdictionary.io/krull-schmidt-failure-0) 

  

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- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A situation in an additive category where an object admits two decompositions as a finite direct sum of indecomposable objects that are not pairwise isomorphic, violating the uniqueness clause of the Krull–Schmidt theorem.