Theorems · Definition · ring theory

Algebra.TensorProduct.piRight

(R : Type u_1) →
  (S : Type u_2) →
    (A : Type u_3) →
      [inst : CommSemiring R] →
        [inst_1 : CommSemiring S] →
          [inst_2 : Algebra R S] →
            [inst_3 : Semiring A] →
              [inst_4 : Algebra R A] →
                [inst_5 : Algebra S A] →
                  [inst_6 : IsScalarTower R S A] →
                    {ι : Type u_4} →
                      (B : ι → Type u_5) →
                        [inst_7 : (i : ι) → Semiring (B i)] →
                          [inst_8 : (i : ι) → Algebra R (B i)] →
                            [Fintype ι] →
                              [DecidableEq ι] →
                                TensorProduct R A ((i : ι) → B i) ≃ₐ[S] (i : ι) → TensorProduct R A (B i)

Tensor product of rings commutes with finite products on the right.

Defined in

Mathlib.RingTheory.TensorProduct.Pi

Cited by

3 results in Mathlib

Foundations

Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringCommSemiringAlgebraSemiringAlgebraAlgebraIsScalarTowerSemiringAlgebraFintypeDecidableEq