Theorems · Definition · field theory

RatFunc.algEquivOfTranscendental

{K : Type u_1} →
  {L : Type u_2} →
    [inst : Field K] →
      [inst_1 : Field L] → [inst_2 : Algebra K L] → (f : L) → Transcendental K f → RatFunc K ≃ₐ[K] ↥K⟮f⟯

Given a transcendental f : L, the K-algebra isomorphism between RatFunc K and L given by sending X to f.

Defined in

Mathlib.FieldTheory.RatFunc.AsPolynomial

Cited by

8 results in Mathlib

Foundations

Depth 118 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldFieldAlgebra