##  [Rack](/rack) 

  ##  [Rack](https://puremath.quantumdictionary.io/rack-0) 

  

 [![Pure Mathematics Dictionary](/sites/default/files/styles/large/public/2026-01/Pure%20Mathematics.png.webp?itok=5pZnFQ59)](/topic-specific-dictionaries/mathematics-logic/pure-mathematics)

- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A set X with a binary operation ▷ such that for all a in X the left translation L_a(x)=a ▷ x is a bijection of X, and the operation is left self-distributive: a ▷ (b ▷ c) = (a ▷ b) ▷ (a ▷ c). Racks capture algebraic self-action without requiring idempotence.