##  [Violation of Serre Condition](/violation-serre-condition) 

  ##  [Violation of Serre Condition](https://algebra.quantumdictionary.io/violation-serre-condition-0) 

  

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- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A situation in which a Noetherian ring or scheme fails to satisfy one of Serre's conditions R_k (regular in codimension k) or S_k (depth at least min(k, local dimension)), indicating defects in regularity or depth-like properties that control extension, duality, and divisor behaviour.