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An integral domain that admits a Euclidean function supporting division with strictly smaller remainder.
The Euclidean function is treated as an existence property, not as chosen structure; not every principal ideal domain is Euclidean.
wp-euclidean-domainnlab-euclidean-domainmilne-algebraic-number-theoryEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Require the existence of a Euclidean function satisfying division with smaller remainder.
Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.
nlab-euclidean-domainwp-integral-domainmilne-algebraic-number-theoryEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
The Euclidean algorithm implies every ideal is principal.
Record a genuine theorem implication that is not part of the target definition; these edges may point toward a weaker structure.
nlab-euclidean-domainwp-pidmilne-algebraic-number-theory