example of PID

Important examples of principal ideal domainsMathworldPlanetmath:

  • The ring of the integers .

  • The ring of polynomials in one variable over a field, i.e. a ring of the form 𝔽[X], where 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 ringsMathworldPlanetmath, 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 2013-03-22 13:33:56
Last modified on 2013-03-22 13:33:56
Owner sleske (997)
Last modified by sleske (997)
Numerical id 5
Author sleske (997)
Entry type Example
Classification msc 13G05