Linked from

The 11 pages that link to Dedekind domain, each with the reason it gives.

• Algebraic number theoryNarrower topic: Rings of integers are Dedekind domains, the setting where nonzero ideals factor uniquely.

• Richard DedekindBroader topic: This algebraic structure generalizes the arithmetic Dedekind developed for rings of integers.

• Prime idealRelated: Its nonzero prime ideals are maximal and factor ideals uniquely into prime ideals.

• Ring of integersRelated: Every ring of integers is a Dedekind domain, enabling unique factorization of ideals.

• Commutative algebraBroader topic: Dedekind domains model rings of integers, where ideals factor uniquely into prime ideals.

• Ideal class groupNarrower topic: Every nonzero fractional ideal is invertible, making the quotient a group.

• IdealRelated: Its ideal factorization extends integer prime factorization to broader number systems.

• Dedekind cutCompared with: Despite sharing Dedekind’s name, this algebraic structure is unrelated to cuts of rationals.

• Ernst KummerRelated: Dedekind later recast Kummer’s ideal numbers as ideals with rigorous ring-theoretic foundations.

• Dirichlet's unit theoremRelated: Rings of integers are Dedekind domains, placing their unit groups in a rich ideal theory.

• Hilbert class fieldRelated: The ring of integers is a Dedekind domain, enabling ideal-theoretic class field constructions.