##  [Artin Reciprocity Law](/artin-reciprocity-law) 

  ##  [Artin Reciprocity Law](https://puremath.quantumdictionary.io/artin-reciprocity-law-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A central statement of global class field theory that constructs a canonical reciprocity map from the idele class group of a global field to the abelianized Galois group of its maximal abelian extension, thereby relating continuous characters of ideles to abelian extensions and generalizing quadratic reciprocity.