Theorems · Definition · field theory

AlgebraicIndependent.aevalEquiv

{ι : Type u_1} →
  {R : Type u_3} →
    {A : Type u_5} →
      {x : ι → A} →
        [inst : CommRing R] →
          [inst_1 : CommRing A] →
            [inst_2 : Algebra R A] → AlgebraicIndependent R x → MvPolynomial ι R ≃ₐ[R] ↥(Algebra.adjoin R (Set.range x))

Canonical isomorphism between polynomials and the subalgebra generated by algebraically independent elements.

Defined in

Mathlib.RingTheory.AlgebraicIndependent.Defs

Cited by

17 results in Mathlib

Foundations

Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebra