Theorems · Theorem · number theory
IsCyclotomicExtension.Rat.map_eq_span_zeta_sub_one_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] {ζ : K} (hζ : IsPrimitiveRoot ζ (p ^ (k + 1))),
Ideal.map (algebraMap ℤ (NumberField.RingOfIntegers K)) (Ideal.span {↑p}) =
Ideal.span {hζ.toInteger - 1} ^ Module.finrank ℚ K- Cited by
- 1 results in Mathlib
- Foundations
- Depth 221 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites46
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Idealstatement and proof · cited by 4,748
- Algebra.algebraMapstatement and proof · cited by 4,706
- MonoidHomproof · cited by 3,629
- Finset.univproof · cited by 3,473
- Factstatement and proof · cited by 2,726
- Finset.prodproof · cited by 2,356
- Nat.Primestatement and proof · cited by 2,059
- Module.finrankstatement and proof · cited by 1,770
Cited by1
Results whose statement or proof uses this declaration.
- IsCyclotomicExtension.Rat.ramificationIdx_span_zeta_sub_oneproof · cited by 4