Theorems · Definition · field theory

IntermediateField.restrictAlgEquiv

{K : Type u_1} →
  {L : Type u_2} →
    [inst : Field K] →
      [inst_1 : Field L] →
        [inst_2 : Algebra K L] → {F E : IntermediateField K L} → (h : F ≤ E) → ↥F ≃ₐ[K] ↥(IntermediateField.restrict h)

F is equivalent to F as an intermediate field of E / K.

Defined in: Mathlib.FieldTheory.IntermediateField.Basic
Cited by: 2 results in Mathlib
Foundations: Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field Field Algebra

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Cites7

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.inclusionproof · cited by 32
AlgEquiv.ofInjectiveFieldproof · cited by 19
IntermediateField.restrictstatement · cited by 4

Cited by3

Results whose statement or proof uses this declaration.

IntermediateField.LinearDisjoint.of_inf_eq_botproof · cited by 2
IntermediateField.finrank_eq_fixingSubgroup_indexproof · cited by 1
IntermediateField.restrict_algEquivproof · cited by 0