Linked from

The 13 pages that link to Ideal class group, each with the reason it gives.

• Algebraic number theoryRelated: Its elements record exactly how far the ring of integers is from unique element factorization.

• Ring of integersRelated: It measures the failure of elements in the ring to have unique factorization.

• Class field theoryRelated: Its elements measure the obstruction to unique factorization and identify unramified abelian extensions.

• Dedekind domainRelated: It measures precisely how far a Dedekind domain is from being a principal ideal domain.

• Ernst KummerRelated: Its finiteness and structure capture the obstruction that Kummer’s ideal numbers addressed.

• Algebraic integerRelated: It captures factorization failures that arise in algebraic-integer rings.

• Unique factorizationRelated: Nontrivial class groups help explain why element factorization can fail in number rings.

• Algebraic number fieldRelated: It records a central obstruction to unique factorization among algebraic integers.

• Dirichlet's unit theoremRelated: Unit computations help determine class groups through bounds and ideal relations.

• Hilbert class fieldNarrower topic: Its elements correspond exactly to automorphisms of the Hilbert class field.

• Class number formulaRelated: Its order is the class number appearing in the formula.

• Kummer–Vandiver conjectureNarrower topic: Its order is the class number whose divisibility the conjecture restricts.

• Stark–Heegner theoremRelated: Class number one means this group is trivial.