Theorems · Theorem · number theory
IsCyclotomicExtension.numberField
∀ (S : Set ℕ) (K : Type w) (L : Type z) [inst : Field K] [inst_1 : Field L] [inst_2 : Algebra K L] [h : NumberField K] [Finite ↑S] [IsCyclotomicExtension S K L], NumberField L
A cyclotomic finite extension of a number field is a number field.
- Defined in
- Mathlib.NumberTheory.Cyclotomic.Basic
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 138 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Set.Elemstatement and proof · cited by 7,166
- Finitestatement and proof · cited by 3,029
- NumberFieldstatement and proof · cited by 653
- IsCyclotomicExtensionstatement and proof · cited by 220
Cited by19
Results whose statement or proof uses this declaration.
- IsCyclotomicExtension.Rat.nrComplexPlaces_eq_totient_div_twostatement and proof · cited by 4
- IsPrimitiveRoot.norm_toInteger_pow_sub_one_of_prime_pow_ne_twoproof · cited by 3
- IsCyclotomicExtension.Rat.nrRealPlaces_eq_zerostatement and proof · cited by 3
- IsCyclotomicExtension.Rat.adjoin_singleton_eq_topproof · cited by 3
- IsPrimitiveRoot.norm_toInteger_sub_one_of_eq_two_powproof · cited by 2
- IsCyclotomicExtension.Rat.discr_primestatement · cited by 2
- IsCyclotomicExtension.Rat.discr_prime_powstatement and proof · cited by 2
- IsPrimitiveRoot.finite_quotient_span_sub_oneproof · cited by 1
- IsPrimitiveRoot.norm_toInteger_pow_sub_one_of_twoproof · cited by 1
- IsPrimitiveRoot.norm_toInteger_sub_one_eq_oneproof · cited by 1
- IsCyclotomicExtension.Rat.discrstatement and proof · cited by 1
- IsCyclotomicExtension.Rat.discr_prime_pow_succstatement · cited by 1