##  [Integral Domain](/integral-domain) 

  ##  [Integral Domain](https://puremath.quantumdictionary.io/integral-domain-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 nonzero commutative ring with unity that has no nonzero zero divisors; equivalently, a commutative ring R with 1 ≠ 0 such that ab = 0 implies a = 0 or b = 0.

 

 

 

 

 





 

 



 ##  [Integral Domain](https://algebra.quantumdictionary.io/integral-domain-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 commutative ring with unity that has no nonzero zero divisors; equivalently, cancellation holds for nonzero factors.