##  [Principal Ideal Domain](/principal-ideal-domain) 

  ##  [Principal Ideal Domain](https://mathlogic.quantumdictionary.io/principal-ideal-domain-0) 

  

 [![Mathematics & Logic Dictionary](/sites/default/files/styles/large/public/2026-01/Mathematics%20%26%20Logic.png.webp?itok=UhtTRPnp)](/topic-specific-dictionaries/natural-formal-sciences/mathematics-logic)

- Natural & Formal Sciences -

**Mathematics & Logic Dictionary**

 







 

 

 

 



 

 

 

 

Definition

An integral domain in which every ideal is principal, i.e., can be generated by a single element; commonly abbreviated PID.

 

 

 

 

 





 

 



 ##  [Principal Ideal Domain](https://algebra.quantumdictionary.io/principal-ideal-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

An integral domain in which every ideal is generated by a single element; often abbreviated PID.