Theorems · Theorem · number theory
IsPrimitiveRoot.intermediateField_adjoin_isCyclotomicExtension
∀ (K : Type w) {L : Type z} [inst : Field K] [inst_1 : Field L] [inst_2 : Algebra K L] [Algebra.IsIntegral K L] {n : ℕ}
[NeZero n] {ζ : L}, IsPrimitiveRoot ζ n → IsCyclotomicExtension {n} K ↥K⟮ζ⟯- Defined in
- Mathlib.NumberTheory.Cyclotomic.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 140 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Subalgebraproof · cited by 1,353
- IntermediateFieldstatement · cited by 988
- IntermediateField.adjoinstatement · cited by 382
- IsPrimitiveRootstatement and proof · cited by 356
- Algebra.IsIntegralstatement and proof · cited by 224
- IsCyclotomicExtensionstatement and proof · cited by 220
- Algebra.IsAlgebraic.isAlgebraicproof · cited by 51
- IntermediateField.adjoin_simple_toSubalgebra_of_isAlgebraicproof · cited by 7
- IsPrimitiveRoot.adjoin_isCyclotomicExtensionproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- IsCyclotomicExtension.Rat.adjoin_singleton_eq_topproof · cited by 3
- IsCyclotomicExtension.Rat.discrproof · cited by 1
- IsPrimitiveRoot.prime_dvd_of_dvd_norm_sub_oneproof · cited by 1
- IsCyclotomicExtension.Rat.isCMFieldproof · cited by 0