##  [Loop](/loop) 

  ##  [Loop](https://puremath.quantumdictionary.io/loop-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A quasigroup that has a two-sided identity element e satisfying e * a = a * e = a for all a. A loop need not be associative, but it retains unique left and right division combined with a neutral element.