##  [Dedekind Domain](/dedekind-domain) 

  ##  [Dedekind Domain](https://puremath.quantumdictionary.io/dedekind-domain-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A Dedekind domain is an integral domain that is Noetherian, integrally closed in its field of fractions, and of Krull dimension one; equivalently every nonzero proper ideal factors uniquely as a product of prime ideals. Dedekind domains provide the natural setting for ideal factorization in algebraic number theory.