Theorems · Theorem · number theory
IsCyclotomicExtension.Rat.adjoin_singleton_eq_top
∀ {n : ℕ} {K : Type u} [inst : Field K] [inst_1 : CharZero K] [hn : NeZero n] [hK : IsCyclotomicExtension {n} ℚ K]
{ζ : K} (hζ : IsPrimitiveRoot ζ n), ℤ[hζ.toInteger] = ⊤- Cited by
- 3 results in Mathlib
- Foundations
- Depth 321 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites32
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Top.topstatement and proof · cited by 9,680
- Fieldstatement and proof · cited by 7,404
- Factproof · cited by 2,726
- mul_commproof · cited by 2,262
- Nat.Primeproof · cited by 2,059
- Subalgebrastatement and proof · cited by 1,353
- CharZerostatement and proof · cited by 932
- NumberFieldproof · cited by 653
- AlgEquiv.symmproof · cited by 615
- Algebra.adjoinstatement and proof · cited by 535
- NumberField.RingOfIntegersstatement and proof · cited by 413
Cited by3
Results whose statement or proof uses this declaration.
- IsCyclotomicExtension.Rat.isIntegralClosure_adjoin_singletonproof · cited by 2
- IsCyclotomicExtension.Rat.ramificationIdx_eq_of_not_dvdproof · cited by 1
- IsCyclotomicExtension.Rat.inertiaDeg_eq_of_not_dvdproof · cited by 1