Theorems · Definition · ring theory

Algebra.TensorProduct.prodRight

(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] →
                    (B : Type u_6) →
                      (C : Type u_7) →
                        [inst_7 : Semiring B] →
                          [inst_8 : Semiring C] →
                            [inst_9 : Algebra R B] →
                              [inst_10 : Algebra R C] →
                                TensorProduct R A (B × C) ≃ₐ[S] TensorProduct R A B × TensorProduct R A C

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

Defined in

Mathlib.RingTheory.TensorProduct.Pi

Cited by

5 results in Mathlib

Foundations

Depth 78 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringCommSemiringAlgebraSemiringAlgebraAlgebraIsScalarTowerSemiringSemiringAlgebraAlgebra