Theorems · Theorem · number theory
isCyclotomicExtension_singleton_iff_eq_adjoin
∀ (n : ℕ) [NeZero n] {A : Type u} {B : Type v} [inst : CommRing A] [inst_1 : CommRing B] [inst_2 : Algebra A B]
[IsDomain B] (C : Subalgebra A B) {ζ : B}, IsPrimitiveRoot ζ n → (IsCyclotomicExtension {n} A ↥C ↔ C = A[ζ])- Defined in
- Mathlib.NumberTheory.Cyclotomic.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 144 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- SetLike.coeproof · cited by 8,199
- Set.ofPredproof · cited by 6,101
- IsDomainstatement and proof · cited by 2,196
- le_antisymmproof · cited by 2,068
- Subalgebrastatement and proof · cited by 1,353
- Algebra.adjoinstatement and proof · cited by 535
- IsPrimitiveRootstatement and proof · cited by 356
- IsCyclotomicExtensionstatement · cited by 220
- Set.singleton_subset_iffproof · cited by 206
Cited by3
Results whose statement or proof uses this declaration.
- IsCyclotomicExtension.lcm_supproof · cited by 1
- IsCyclotomicExtension.le_of_dvdproof · cited by 1
- IntermediateField.isCyclotomicExtension_singleton_iff_eq_adjoinproof · cited by 0