Theorems · Theorem · number theory
IsPrimitiveRoot.adjoin_isCyclotomicExtension
∀ (A : Type u) {B : Type v} [inst : CommRing A] [inst_1 : CommRing B] [inst_2 : Algebra A B] {ζ : B} {n : ℕ} [NeZero n],
IsPrimitiveRoot ζ n → IsCyclotomicExtension {n} A ↥A[ζ]- Defined in
- Mathlib.NumberTheory.Cyclotomic.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
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
- Set.ofPredproof · cited by 6,101
- Subalgebrastatement · cited by 1,353
- Algebra.adjoinstatement and proof · cited by 535
- IsPrimitiveRootstatement and proof · cited by 356
- IsCyclotomicExtensionstatement · cited by 220
- Set.mem_singletonproof · cited by 183
- Set.mem_singleton_iffproof · cited by 172
- Algebra.subset_adjoinproof · cited by 109
- Subtype.coe_mkproof · cited by 81
Cited by3
Results whose statement or proof uses this declaration.
- IsPrimitiveRoot.intermediateField_adjoin_isCyclotomicExtensionproof · cited by 4
- IsPrimitiveRoot.lcm_totient_le_finrankproof · cited by 1
- IsCyclotomicExtension.lcm_supproof · cited by 1