##  [Capitulation](/capitulation) 

  ##  [Capitulation](https://puremath.quantumdictionary.io/capitulation-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The phenomenon in algebraic number theory where ideal classes of a number field become principal in a finite extension field; equivalently, certain elements of the class group map to the trivial class under the transfer (or extension) map, revealing failure of injectivity for class group maps under extension.