##  [Ore Condition](/ore-condition) 

  ##  [Ore Condition](https://puremath.quantumdictionary.io/ore-condition-0) 

  

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**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A criterion for a cancellative semigroup or domain that for every pair of nonzero elements a,b there exist nonzero s,t with as=bt (right Ore) or sa=tb (left Ore), enabling construction of a localization or ring of fractions in the noncommutative setting.