##  [Idèle](/idele) 

  ##  [Idèle](https://puremath.quantumdictionary.io/idele-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

An idèle is an invertible element of the adèle ring of a global field: a tuple (x_v) of nonzero elements x_v in each local completion such that x_v is a unit for all but finitely many places. The idèles form a topological multiplicative group used in global class field theory.