##  [Non-Split Extension](/non-split-extension) 

  ##  [Non-Split Extension](https://puremath.quantumdictionary.io/non-split-extension-0) 

  

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**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

An exact extension 0 -> A -> E -> B -> 0 which is not isomorphic to the direct or trivial extension A ⊕ B (or the semidirect/trivial splitting in the relevant category); equivalently, its class in the appropriate Ext or classification group is nonzero.