Theorems · Definition · field theory

AlgHom.equivFieldRange

{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'] → (f : L →ₐ[K] L') → L ≃ₐ[K] ↥f.fieldRange

The isomorphism from L to the field range of the AlgHom f, sending x to f x.

Defined in

Mathlib.FieldTheory.IntermediateField.Basic

Cited by

4 results in Mathlib

Foundations

Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldFieldFieldAlgebraAlgebra