Theorems · Definition · ring theory

TensorAlgebra.equivDirectSum

{R : Type u_1} →
  {M : Type u_2} →
    [inst : CommSemiring R] →
      [inst_1 : AddCommMonoid M] →
        [inst_2 : Module R M] → TensorAlgebra R M ≃ₐ[R] DirectSum ℕ fun n => TensorPower R n M

The tensor algebra is isomorphic to a direct sum of tensor powers.

Defined in

Mathlib.LinearAlgebra.TensorAlgebra.ToTensorPower

Cited by

2 results in Mathlib

Foundations

Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoidModule