##  [Division Ring](/division-ring) 

  ##  [Division Ring](https://puremath.quantumdictionary.io/division-ring-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 ring with unity in which every nonzero element has a multiplicative inverse, but multiplication need not be commutative; also called a skew field.

 

 

 

 

 





 

 



 ##  [Division Ring](https://algebra.quantumdictionary.io/division-ring-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

An associative ring with unity in which every nonzero element has a multiplicative inverse; multiplication need not be commutative. Often called a skew field.