PID
A principal ideal domain is an integral domain where every ideal is a principal ideal.
In a PID, an ideal is maximal if and only if is irreducible (and prime since any PID is also a UFD (http://planetmath.org/PIDsAreUFDs)).
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 |