Theorems · Definition · field theory
IntermediateField.equivOfEq
{F : Type u_4} →
[inst : Field F] →
{E : Type u_5} → [inst_1 : Field E] → [inst_2 : Algebra F E] → {S T : IntermediateField F E} → S = T → ↥S ≃ₐ[F] ↥TConstruct an algebra isomorphism from an equality of intermediate fields.
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 61 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
- AlgEquivstatement · cited by 1,681
- IntermediateFieldstatement and proof · cited by 988
- IntermediateField.toSubalgebraproof · cited by 134
- Subalgebra.equivOfEqproof · cited by 15
Cited by25
Results whose statement or proof uses this declaration.
- AlgebraicIndependent.aevalEquivFieldproof · cited by 5
- IntermediateField.equivOfEq_applystatement and proof · cited by 3
- RatFunc.Luroth.algEquivproof · cited by 3
- IsCyclotomicExtension.isSeparableproof · cited by 3
- Field.powerBasisOfFiniteOfSeparableproof · cited by 3
- IntermediateField.equivMapproof · cited by 2
- IntermediateField.exists_algHom_of_adjoin_splitsproof · cited by 2
- RatFunc.IntermediateField.adjoinXEquivproof · cited by 2
- IntermediateField.exists_algHom_of_adjoin_splits'proof · cited by 1
- IntermediateField.exists_algHom_of_adjoin_splits_of_aevalproof · cited by 1
- Field.Emb.Cardinal.equivLimproof · cited by 1
- Field.Emb.Cardinal.equivSuccproof · cited by 1