Theorems · Theorem · number theory

IsCyclotomicExtension.Rat.eq_span_zeta_sub_one_of_liesOver

∀ (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] {ζ : K} (hζ : IsPrimitiveRoot ζ (p ^ (k + 1)))
  (P : Ideal (NumberField.RingOfIntegers K)) [hP₁ : P.IsPrime] [hP₂ : P.LiesOver (Ideal.span {↑p})],
  P = Ideal.span {hζ.toInteger - 1}

Defined in

Mathlib.NumberTheory.NumberField.Cyclotomic.Ideal

Cited by

3 results in Mathlib

Foundations

Depth 226 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FactFieldNumberFieldIsCyclotomicExtensionIdeal.IsPrimeIdeal.LiesOver