Theorems · Definition · number theory
CyclotomicField
ℕ → (K : Type w) → [Field K] → Type w
Given a nonzero n : ℕ and a field K, we define CyclotomicField n K as the
splitting field of cyclotomic n K. If n is nonzero in K, it has
the instance IsCyclotomicExtension {n} K (CyclotomicField n K).
- Defined in
- Mathlib.NumberTheory.Cyclotomic.Basic
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fieldstatement and proof · cited by 7,404
- Polynomial.cyclotomicproof · cited by 130
- Polynomial.SplittingFieldproof · cited by 42
Cited by23
Results whose statement or proof uses this declaration.
- CyclotomicRingproof · cited by 6
- AddChar.PrimitiveAddChar.charstatement · cited by 4
- AddChar.PrimitiveAddChar.primstatement · cited by 4
- AddChar.FiniteField.primitiveCharproof · cited by 3
- IsCyclotomicExtension.Rat.cyclotomicRing_isIntegralClosure_of_prime_powstatement and proof · cited by 1
- Char.card_pow_cardproof · cited by 1
- AddChar.FiniteField.primitiveChar_to_Complexproof · cited by 1
- AddChar.PrimitiveAddChar.mk.injstatement and proof · cited by 1
- AddChar.PrimitiveAddChar.mk.noConfusionstatement and proof · cited by 1
- FiniteField.two_pow_cardproof · cited by 1
- IsCyclotomicExtension.Rat.cyclotomicRing_isIntegralClosurestatement and proof · cited by 0
- IsCyclotomicExtension.Rat.cyclotomicRing_isIntegralClosure_of_primestatement and proof · cited by 0