A principal ideal domainMathworldPlanetmath is an integral domainMathworldPlanetmath where every ideal is a principal idealMathworldPlanetmathPlanetmathPlanetmath.

In a PID, an ideal (p) is maximal if and only if p is irreduciblePlanetmathPlanetmath (and prime since any PID is also a UFD (

Note that subrings of PIDs are not necessarily PIDs. (There is an example of this within the entry biquadratic field.)

Title PID
Canonical name PID
Date of creation 2013-03-22 11:56:25
Last modified on 2013-03-22 11:56:25
Owner mps (409)
Last modified by mps (409)
Numerical id 13
Author mps (409)
Entry type Definition
Classification msc 16D25
Classification msc 13G05
Classification msc 11N80
Classification msc 13A15
Synonym principal ideal domain
Related topic UFD
Related topic Irreducible
Related topic Ideal
Related topic IntegralDomain
Related topic EuclideanRing
Related topic EuclideanValuation
Related topic ProofThatAnEuclideanDomainIsAPID
Related topic WhyEuclideanDomains