Theorems · Definition · field theory
IntermediateField.fixedField
{F : Type u_1} →
[inst : Field F] →
{E : Type u_2} → [inst_1 : Field E] → [inst_2 : Algebra F E] → Subgroup Gal(E/F) → IntermediateField F EThe intermediate field fixed by a subgroup.
- Defined in
- Mathlib.FieldTheory.Galois.Basic
- Cited by
- 25 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Subgroupstatement and proof · cited by 3,593
- AlgEquivstatement and proof · cited by 1,681
- IntermediateFieldstatement · cited by 988
- FixedPoints.intermediateFieldproof · cited by 18
Cited by34
Results whose statement or proof uses this declaration.
- IsGalois.intermediateFieldEquivSubgroupproof · cited by 10
- IntermediateField.le_iff_lestatement and proof · cited by 5
- IntermediateField.mem_fixedField_iffstatement · cited by 4
- IntermediateField.finrank_fixedField_eq_cardstatement and proof · cited by 3
- IntermediateField.fixingSubgroup_fixedFieldstatement and proof · cited by 3
- InfiniteGalois.fixedField_fixingSubgroupstatement and proof · cited by 3
- IsGalois.fixedField_fixingSubgroupstatement and proof · cited by 2
- IsGalois.fixedField_topstatement and proof · cited by 2
- IsGalois.of_fixedField_eq_botstatement and proof · cited by 2
- IsGalois.tfaestatement and proof · cited by 2
- InfiniteGalois.normal_iff_isGaloisproof · cited by 2
- InfiniteGalois.restrict_fixedFieldstatement and proof · cited by 2