principal ideal ring

A commutative ring R in which all ideals are principal (, i.e. ( generated by ( a single ring element, is called a principal ideal ring.  If R is also an integral domainMathworldPlanetmath, it is a principal ideal domainMathworldPlanetmath.

Some well-known principal ideal rings are the ring of integers, its factor rings /n, and any polynomial ring over a field.

Title principal ideal ring
Canonical name PrincipalIdealRing
Date of creation 2013-03-22 14:33:16
Last modified on 2013-03-22 14:33:16
Owner Wkbj79 (1863)
Last modified by Wkbj79 (1863)
Numerical id 7
Author Wkbj79 (1863)
Entry type Definition
Classification msc 13F10
Classification msc 13A15
Synonym principal ring
Related topic CriterionForCyclicRingsToBePrincipalIdealRings