##  [Adèle](/index.php/adele) 

  ##  [Adèle](https://puremath.quantumdictionary.io/adele-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

An adèle of a global field K is an element of the restricted (or restricted direct) product of the completions K_v at all places v of K, where for all but finitely many nonarchimedean v the component lies in the local ring of integers O_v. The ring of adèles combines simultaneously the local completions with an 'almost integral' condition.