Linked from

The 31 pages that link to Algebraic number theory, each with the reason it gives.

• Fermat's Last TheoremNarrower topic: Kummer's approach to Fermat's equation helped develop this field's central methods.

• Algebraic numberNarrower topic: It develops the arithmetic of algebraic numbers into a field of study.

• Richard DedekindNarrower topic: Dedekind’s ideal theory became a central framework for the subject.

• Pierre de FermatRelated: The eventual proof of Fermat’s Last Theorem drew on tools developed in this branch.

• Abstract algebraRelated: It applies rings and fields to questions about integer solutions and prime factorization.

• Cyclotomic polynomialNarrower topic: Cyclotomic polynomials generate central examples of algebraic number fields.

• Quotient ringNarrower topic: Quotient rings help describe prime ideals and residue fields in number rings.

• Commutative ringRelated: Rings of integers provide a central setting for factoring and divisibility questions.

• Ring of integersNarrower topic: Rings of integers provide its central setting for divisibility and prime behavior.

• Commutative algebraRelated: Ideals and localization clarify factorization and divisibility in rings of integers.

• Ideal (ring theory)Narrower topic: Ideals restore unique factorization of elements into a broader factorization theory.

• Ideal class groupNarrower topic: Class groups emerged as a way to organize factorization in number rings.

• Disquisitiones ArithmeticaeNarrower topic: Gauss’s treatment of forms and congruences helped inspire later structural approaches to arithmetic.

• Geometry of numbersCompared with: Its abstract algebraic tools complement the field's geometric treatment of number fields.

• Emil ArtinRelated: This is the setting for Artin’s reciprocity law and much of his research.

• Ernst KummerNarrower topic: Kummer’s ideal numbers helped establish this field’s foundations.

• Richard BrauerRelated: Brauer’s work on algebras and group representations also influenced questions in number theory.

• Algebraic integerNarrower topic: Algebraic integers are its basic arithmetic objects.

• Unique factorizationNarrower topic: It reframes integer factorization as a question about factorization in larger rings.

• Leopold KroneckerNarrower topic: This field unites the arithmetic and algebra that defined much of Kronecker’s research.

• Dirichlet's unit theoremNarrower topic: The theorem is a foundational structural result in this subject.

• Helmut HasseNarrower topic: This is the field in which Hasse developed local methods.

• Hensel's lemmaNarrower topic: The lemma connects congruence calculations to roots in local number fields.

• Ramanujan–Nagell equationNarrower topic: Its proof uses factorization and arithmetic properties of integers in a number field.

• Ring theoryNarrower topic: Rings of integers encode arithmetic beyond the ordinary integers.

• Serge LangRelated: It provides the arithmetic setting for Lang’s work on class field theory and Diophantine questions.

• Siegel's lemmaRelated: The lemma provides controlled relations among algebraic quantities and coefficients.

• Eisenstein's criterionNarrower topic: Irreducibility tests help determine the fields generated by algebraic numbers.

• Birch–Tate conjectureNarrower topic: The conjecture arose within arithmetic investigations of number fields.

• Hasse's theorem on elliptic curvesNarrower topic: Hasse's methods emerged from a number-theoretic setting and influenced later arithmetic geometry.

• Schinzel's theoremNarrower topic: The theorem's prime-modulus behavior extends naturally to arithmetic in number fields.