##  [Capitulation Kernel](/capitulation-kernel) 

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

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The subgroup of the ideal class group of a base global field consisting of those ideal classes that become principal in a specified finite extension; equivalently the kernel of the natural transfer (or capitulation) map from the class group of the base field to the class group of the extension.