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 |