Euclidean domain

A Euclidean domainMathworldPlanetmath is an integral domainMathworldPlanetmath on which a Euclidean valuation can be defined.

Every Euclidean domain is a principal ideal domainMathworldPlanetmath, and therefore also a unique factorization domainMathworldPlanetmath.

Any two elements of a Euclidean domain have a greatest common divisorMathworldPlanetmathPlanetmath, which can be computed using the Euclidean algorithmMathworldPlanetmath.

An example of a Euclidean domain is the ring . Another example is the polynomial ring F[x], where F 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