Theorems · Theorem · number theory

IsCyclotomicExtension.Rat.ncard_primesOver_of_prime_pow

∀ (p k : ℕ) [hp : Fact (Nat.Prime p)] (K : Type u_1) [inst : Field K] [inst_1 : NumberField K]
  [hK : IsCyclotomicExtension {p ^ (k + 1)} ℚ K],
  ((Ideal.span {↑p}).primesOver (NumberField.RingOfIntegers K)).ncard = 1

Defined in: Mathlib.NumberTheory.NumberField.Cyclotomic.Ideal
Cited by: 2 results in Mathlib
Foundations: Depth 225 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Fact Field NumberField IsCyclotomicExtension

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Cites36

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Setstatement · cited by 53,352
Fieldstatement and proof · cited by 7,404
Idealstatement · cited by 4,748
mul_oneproof · cited by 3,885
Factstatement and proof · cited by 2,726
Nat.Primestatement and proof · cited by 2,059
Module.finrankproof · cited by 1,770
AlgEquivproof · cited by 1,681
LT.lt.ne'proof · cited by 1,417
Ideal.spanstatement and proof · cited by 948
Nat.cardproof · cited by 844
NumberFieldstatement and proof · cited by 653

Cited by2

Results whose statement or proof uses this declaration.

IsCyclotomicExtension.Rat.eq_span_zeta_sub_one_of_liesOverproof · cited by 3
IsCyclotomicExtension.Rat.ncard_primesOver_of_primeproof · cited by 0