Theorems · Definition · field theory

IntermediateField.intermediateFieldMap

{K : Type u_1} →
  {L : Type u_2} →
    {L' : Type u_3} →
      [inst : Field K] →
        [inst_1 : Field L] →
          [inst_2 : Field L'] →
            [inst_3 : Algebra K L] →
              [inst_4 : Algebra K L'] →
                (e : L ≃ₐ[K] L') → (E : IntermediateField K L) → ↥E ≃ₐ[K] ↥(IntermediateField.map (↑e) E)

Given an equivalence e : L ≃ₐ[K] L' of K-field extensions and an intermediate field E of L/K, intermediateFieldMap e E is the induced equivalence between E and E.map e.

Defined in

Mathlib.FieldTheory.IntermediateField.Basic

Cited by

2 results in Mathlib

Foundations

Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldFieldFieldAlgebraAlgebra