Theorems · Definition · linear algebra

Module.Basis.tensorProduct

{R : Type u_1} →
  {S : Type u_2} →
    {M : Type u_3} →
      {N : Type u_4} →
        {ι : Type u_5} →
          {κ : Type u_6} →
            [inst : CommSemiring R] →
              [inst_1 : Semiring S] →
                [inst_2 : Algebra R S] →
                  [inst_3 : AddCommMonoid M] →
                    [inst_4 : Module R M] →
                      [inst_5 : Module S M] →
                        [inst_6 : IsScalarTower R S M] →
                          [inst_7 : AddCommMonoid N] →
                            [inst_8 : Module R N] →
                              Module.Basis ι S M → Module.Basis κ R N → Module.Basis (ι × κ) S (TensorProduct R M N)

If b : ι → M and c : κ → N are bases then so is fun i ↦ b i.1 ⊗ₜ c i.2 : ι × κ → M ⊗ N.

Defined in

Mathlib.LinearAlgebra.TensorProduct.Basis

Cited by

19 results in Mathlib

Foundations

Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringSemiringAlgebraAddCommMonoidModuleModuleIsScalarTowerAddCommMonoidModule