Theorems · Theorem · field theory
isGalois_iff
∀ {F : Type u_1} [inst : Field F] {E : Type u_2} [inst_1 : Field E] [inst_2 : Algebra F E],
IsGalois F E ↔ Algebra.IsSeparable F E ∧ Normal F E- Defined in
- Mathlib.FieldTheory.Galois.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 47 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Algebra.IsSeparablestatement and proof · cited by 210
- IsGaloisstatement and proof · cited by 149
- Normalstatement and proof · cited by 92
Cited by2
Results whose statement or proof uses this declaration.
- IsCyclotomicExtension.isGaloisproof · cited by 13
- IsGalois.of_equiv_equivproof · cited by 1