Theorems · Definition · commutative algebra

PiTensorProduct.mul

{ι : Type u_1} →
  {R : Type u_3} →
    {A : ι → Type u_4} →
      [inst : CommSemiring R] →
        [inst_1 : (i : ι) → NonUnitalNonAssocSemiring (A i)] →
          [inst_2 : (i : ι) → Module R (A i)] →
            [∀ (i : ι), SMulCommClass R (A i) (A i)] →
              [∀ (i : ι), IsScalarTower R (A i) (A i)] →
                (PiTensorProduct R fun i => A i) →ₗ[R]
                  (PiTensorProduct R fun i => A i) →ₗ[R] PiTensorProduct R fun i => A i

The multiplication in tensor product of rings is induced by (xᵢ) * (yᵢ) = (xᵢ * yᵢ)

Defined in

Mathlib.RingTheory.PiTensorProduct

Cited by

8 results in Mathlib

Foundations

Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringNonUnitalNonAssocSemiringModuleSMulCommClassIsScalarTower