##  [Semigroup](/semigroup) 

  ##  [Semigroup](https://puremath.quantumdictionary.io/semigroup-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 equipped with an associative binary operation but not necessarily possessing an identity element or inverses.

 

 

 

 

 





 

 



 ##  [Semigroup](https://algebra.quantumdictionary.io/semigroup-1) 

  

 [![Algebra](/sites/default/files/styles/large/public/2026-01/Algebra.png.webp?itok=3pHxBnUF)](/topic-specific-dictionaries/pure-mathematics/algebra)

- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A set equipped with an associative binary operation; a semigroup need not have an identity element or inverses for its elements.