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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] ↥T

Construct an algebra isomorphism from an equality of intermediate fields.

Defined in
Mathlib.FieldTheory.IntermediateField.Basic
Cited by
13 results in Mathlib
Foundations
Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FieldFieldAlgebra

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AlgebraicIndependent.aevalEquivField · cited by 5AlgebraicIndependent.aeva…IntermediateField.equivOfEq_apply · cited by 3IntermediateField.equivOf…RatFunc.Luroth.algEquiv · cited by 3Luroth.algEquivIsCyclotomicExtension.isSeparable · cited by 3IsCyclotomicExtension.isS…Field.powerBasisOfFiniteOfSeparable · cited by 3Field.powerBasisOfFiniteO…IntermediateField.equivMap · cited by 2IntermediateField.equivMapIntermediateField.exists_algHom_of_adjoin_splits · cited by 2IntermediateField.exists_…RatFunc.IntermediateField.adjoinXEquiv · cited by 2IntermediateField.adjoinX…IntermediateField.exists_algHom_of_adjoin_splits' · cited by 1IntermediateField.exists_…IntermediateField.exists_algHom_of_adjoin_splits_of_aeval · cited by 1IntermediateField.exists_…Field.Emb.Cardinal.equivLim · cited by 1Cardinal.equivLimField.Emb.Cardinal.equivSucc · cited by 1Cardinal.equivSuccDifferential.differentialFiniteDimensional · cited by 1Differential.differential…IsCyclotomicExtension.nonempty_algEquiv_adjoin_of_isSepClosed · cited by 1IsCyclotomicExtension.non…IntermediateField.Lifts.nonempty_algHom_of_exist_lifts_finset · cited by 1Lifts.nonempty_algHom_of_…Algebra · cited by 11388AlgebraField · cited by 7404FieldAlgEquiv · cited by 1681AlgEquivIntermediateField · cited by 988IntermediateFieldIntermediateField.toSubalgebra · cited by 134IntermediateField.toSubal…Subalgebra.equivOfEq · cited by 15Subalgebra.equivOfEqIntermediateField.equivOfEqCITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by25

Results whose statement or proof uses this declaration.