Theorems · Definition · field theory
IntermediateField.topEquiv
{F : Type u_1} → [inst : Field F] → {E : Type u_2} → [inst_1 : Field E] → [inst_2 : Algebra F E] → ↥⊤ ≃ₐ[F] EThe top IntermediateField is isomorphic to the field.
This is the intermediate field version of Subalgebra.topEquiv.
- Cited by
- 24 results in Mathlib
- Foundations
- Depth 85 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
- Top.topstatement · cited by 9,680
- Fieldstatement and proof · cited by 7,404
- AlgEquivstatement · cited by 1,681
- IntermediateFieldstatement · cited by 988
- Subalgebra.topEquivproof · cited by 9
Cited by28
Results whose statement or proof uses this declaration.
- IntermediateField.exists_lt_finrank_of_infinite_dimensionalproof · cited by 3
- IsCyclotomicExtension.isSeparableproof · cited by 3
- Field.powerBasisOfFiniteOfSeparableproof · cited by 3
- IsCyclotomicExtension.Rat.adjoin_singleton_eq_topproof · cited by 3
- Subfield.relrank_top_rightproof · cited by 2
- IntermediateField.exists_algHom_of_adjoin_splitsproof · cited by 2
- RatFunc.IntermediateField.adjoinXEquivproof · cited by 2
- IntermediateField.finSepDegree_topproof · cited by 2
- IntermediateField.fg_top_iffproof · cited by 2
- IntermediateField.insepDegree_topproof · cited by 1
- IsCyclotomicExtension.Rat.discrproof · cited by 1
- IntermediateField.exists_algHom_of_adjoin_splits'proof · cited by 1