example of PID
Important examples of principal ideal domains^{}:

•
The ring of the integers $\mathbb{Z}$.

•
The ring of polynomials in one variable over a field, i.e. a ring of the form $\mathbb{F}[X]$, where $\mathbb{F}$ is a field. Note that the ring of polynomials in more than one variable over a field is never a PID.
Both of these examples are actually examples of Euclidean rings^{}, which are always PIDs. There are, however, more complicated examples of PIDs which are not Euclidean rings.
Title  example of PID 

Canonical name  ExampleOfPID 
Date of creation  20130322 13:33:56 
Last modified on  20130322 13:33:56 
Owner  sleske (997) 
Last modified by  sleske (997) 
Numerical id  5 
Author  sleske (997) 
Entry type  Example 
Classification  msc 13G05 