Theorems · Theorem · number theory
IsCyclotomicExtension.isAbelianGalois
∀ (S : Set ℕ) (K : Type w) (L : Type z) [inst : Field K] [inst_1 : Field L] [inst_2 : Algebra K L] [IsCyclotomicExtension S K L], IsAbelianGalois K L
Cyclotomic extensions are abelian.
- Defined in
- Mathlib.NumberTheory.Cyclotomic.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 199 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- AlgEquivproof · cited by 1,681
- IsCyclotomicExtensionstatement and proof · cited by 220
- IsGaloisproof · cited by 149
- IsMulCommutativeproof · cited by 95
- IsCyclotomicExtension.isGaloisproof · cited by 13
- IsAbelianGaloisstatement · cited by 10
- IsCyclotomicExtension.isMulCommutativeproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- IsCyclotomicExtension.Rat.isCMFieldproof · cited by 0