Linked from

The 15 pages that link to Ring of integers, each with the reason it gives.

• Algebraic number theoryBroader topic: It supplies the canonical domain for arithmetic in each number field.

• Richard DedekindRelated: Dedekind analyzed these rings as the natural setting for number-field arithmetic.

• Ring (mathematics)Broader topic: It is the basic example of a commutative ring with identity.

• Ideal class groupRelated: Its ideals provide the standard arithmetic setting for class groups.

• Dedekind domainNarrower topic: Every ring of integers of a number field is a Dedekind domain.

• Dedekind zeta functionRelated: The function sums ideals in this ring rather than ideals in the field itself.

• Ernst KummerRelated: Kummer’s factorization difficulties arose in rings of integers of cyclotomic fields.

• Algebraic integerBroader topic: It collects the algebraic integers belonging to each number field.

• Algebraic number fieldBroader topic: It provides the natural domain for integer-like arithmetic inside the field.

• Dirichlet's unit theoremRelated: Its invertible elements are the units whose rank the theorem computes.

• Hilbert class fieldRelated: Its ideals supply the arithmetic objects used in the class group and Artin map.

• DiscriminantRelated: The discriminant belongs to this ring’s arithmetic structure, not merely to an arbitrary field basis.

• Ring theoryBroader topic: It is the basic example whose ideals and quotients model arithmetic.

• Birch–Tate conjectureRelated: This is the ring whose second K-group appears in the statement.

• Stark–Heegner theoremRelated: Its ideals determine the class number and discriminant used in the classification.