##  [Dirichlet's Unit Theorem](/dirichlets-unit-theorem) 

  ##  [Dirichlet's Unit Theorem](https://puremath.quantumdictionary.io/dirichlets-unit-theorem-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The structural description of the unit group O_K^× of the ring of integers of a number field K: O_K^× is the direct product of the finite group of roots of unity in K and a free abelian group of rank r+s−1, where r is the number of real embeddings of K and s the number of pairs of complex embeddings.