Theorems · Definition · linear algebra

TensorProduct.equivFinsuppOfBasisRight

{R : Type u_1} →
  {M : Type u_3} →
    {N : Type u_4} →
      {κ : Type u_6} →
        [inst : CommSemiring R] →
          [inst_1 : AddCommMonoid M] →
            [inst_2 : Module R M] →
              [inst_3 : AddCommMonoid N] →
                [inst_4 : Module R N] → [DecidableEq κ] → Module.Basis κ R N → TensorProduct R M N ≃ₗ[R] κ →₀ M

If {𝒞ᵢ} is a basis for the module N, then every elements of x ∈ M ⊗ N can be uniquely written as ∑ᵢ mᵢ ⊗ 𝒞ᵢ for some mᵢ ∈ M.

Defined in

Mathlib.LinearAlgebra.TensorProduct.Basis

Cited by

8 results in Mathlib

Foundations

Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoidModuleAddCommMonoidModuleDecidableEq