Theorems · Definition · ring theory

IsSymmetricAlgebra.equiv

{R : Type u_1} →
  {M : Type u_2} →
    [inst : CommSemiring R] →
      [inst_1 : AddCommMonoid M] →
        [inst_2 : Module R M] →
          {A : Type u_3} →
            [inst_3 : CommSemiring A] →
              [inst_4 : Algebra R A] → {f : M →ₗ[R] A} → IsSymmetricAlgebra f → SymmetricAlgebra R M ≃ₐ[R] A

For f : M →ₗ[R] A, construct the algebra isomorphism SymmetricAlgebra R M ≃ₐ[R] A from IsSymmetricAlgebra f.

Defined in

Mathlib.LinearAlgebra.SymmetricAlgebra.Basic

Cited by

7 results in Mathlib

Foundations

Depth 53 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoidModuleCommSemiringAlgebra