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A Noetherian, integrally closed integral domain of Krull dimension one.
This atlas uses the dimension-one convention, excluding fields; some references allow dimension at most one and hence include fields.
wp-dedekind-domainnlab-dedekind-domainstacks-dedekindmilne-algebraic-number-theoryEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Require Noetherianity, integral closure, and Krull dimension one.
Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.
nlab-dedekind-domainmilne-algebraic-number-theoryThis is an authored directed relation from the source endpoint to the target endpoint.
The ring of integers of a number field is a Dedekind domain.
Record a genuine theorem implication that is not part of the target definition; these edges may point toward a weaker structure.
wp-ring-integersnlab-dedekind-domainstacks-dedekindmilne-algebraic-number-theoryEach relation below starts at this concept.
No direct relations are authored in this direction.