##  [Failure of Cancellation](/failure-cancellation) 

  ##  [Failure of Cancellation](https://algebra.quantumdictionary.io/failure-cancellation-0) 

  

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- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The phenomenon in an additive category (e.g., modules) where A ⊕ C ≅ B ⊕ C does not imply A ≅ B; that is, direct-sum cancellation fails and isomorphism after adding the same summand does not force isomorphism of the original summands.