Theorems · Definition · ring theory

SymmetricAlgebra.equivMvPolynomial

{κ : Type uκ} →
  {R : Type uR} →
    {M : Type uM} →
      [inst : CommSemiring R] →
        [inst_1 : AddCommMonoid M] →
          [inst_2 : Module R M] → Module.Basis κ R M → SymmetricAlgebra R M ≃ₐ[R] MvPolynomial κ R

SymmetricAlgebra.equivMvPolynomial gives an algebra isomorphism between the symmetric algebra over a free module and multivariate polynomials over a basis. This is analogous to TensorAlgebra.equivFreeAlgebra.

Defined in

Mathlib.LinearAlgebra.SymmetricAlgebra.Basis

Cited by

5 results in Mathlib

Foundations

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

Assumes

CommSemiringAddCommMonoidModule