##  [Failure of Idempotent Lifting](/index.php/failure-idempotent-lifting) 

  ##  [Failure of Idempotent Lifting](https://algebra.quantumdictionary.io/failure-idempotent-lifting-0) 

  

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- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A situation in a ring or algebra surjection π: A → A/I where an idempotent e ∈ A/I (e^2 = e) does not admit any idempotent p ∈ A with π(p) = e; the quotient contains a projector that has no idempotent preimage in the source.