Theorems · Theorem · number theory
IsCyclotomicExtension.adjoin_roots_cyclotomic_eq_adjoin_root_cyclotomic
∀ {A : Type u} {B : Type v} [inst : CommRing A] [inst_1 : CommRing B] [inst_2 : Algebra A B] {n : ℕ} [NeZero n]
[inst_4 : IsDomain B] {ζ : B}, IsPrimitiveRoot ζ n → Algebra.adjoin A ((Polynomial.cyclotomic n A).rootSet B) = A[ζ]- Defined in
- Mathlib.NumberTheory.Cyclotomic.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 207 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites29
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
- Polynomialproof · cited by 5,681
- Algebra.algebraMapproof · cited by 4,706
- IsDomainstatement and proof · cited by 2,196
- le_antisymmproof · cited by 2,068
- Subalgebrastatement · cited by 1,353
- Polynomial.mapproof · cited by 806
- Polynomial.evalproof · cited by 796
- Algebra.adjoinstatement and proof · cited by 535
- IsPrimitiveRootstatement and proof · cited by 356
Cited by2
Results whose statement or proof uses this declaration.
- IsCyclotomicExtension.adjoin_primitive_root_eq_topproof · cited by 0
- CyclotomicRing.eq_adjoin_primitive_rootproof · cited by 0