Euclidean domain
A Euclidean domain
is an integral domain
on which a Euclidean valuation can be defined.
Every Euclidean domain is a principal ideal domain,
and therefore also a unique factorization domain
.
Any two elements of a Euclidean domain have a greatest common divisor,
which can be computed using the Euclidean algorithm
.
An example of a Euclidean domain is the ring . Another example is the polynomial ring , where is any field. Every field is also a Euclidean domain.
| Title | Euclidean domain |
| Canonical name | EuclideanDomain |
| Date of creation | 2013-03-22 12:40:42 |
| Last modified on | 2013-03-22 12:40:42 |
| Owner | yark (2760) |
| Last modified by | yark (2760) |
| Numerical id | 13 |
| Author | yark (2760) |
| Entry type | Definition |
| Classification | msc 13F07 |
| Synonym | Euclidean ring |
| Related topic | PID |
| Related topic | UFD |
| Related topic | EuclidsAlgorithm |
| Related topic | Ring |
| Related topic | IntegralDomain |
| Related topic | EuclideanValuation |
| Related topic | WhyEuclideanDomains |