Theorems · Theorem · number theory
IntermediateField.isCyclotomicExtension_singleton_iff_eq_adjoin
∀ (n : ℕ) [NeZero n] (K : Type w) (L : Type z) [inst : Field K] [inst_1 : Field L] [inst_2 : Algebra K L]
(F : IntermediateField K L) {ζ : L}, IsPrimitiveRoot ζ n → (IsCyclotomicExtension {n} K ↥F ↔ F = K⟮ζ⟯)- Defined in
- Mathlib.NumberTheory.Cyclotomic.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 145 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites16
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 and proof · cited by 988
- IntermediateField.adjoinstatement · cited by 382
- IsPrimitiveRootstatement and proof · cited by 356
- IsCyclotomicExtensionstatement and proof · cited by 220
- IntermediateField.toSubalgebraproof · cited by 134
- NeZero.posproof · cited by 57
- IsIntegral.tower_topproof · cited by 30
- IsIntegral.isAlgebraicproof · cited by 18
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