# 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 ExampleOfPID 2013-03-22 13:33:56 2013-03-22 13:33:56 sleske (997) sleske (997) 5 sleske (997) Example msc 13G05