Theorems · Definition · ring theory

AddMonoidAlgebra.rTensorEquivAlgEquiv

(R : Type u_1) →
  {M : Type u_2} →
    (S : Type u_4) →
      (A : Type u_5) →
        (B : Type u_6) →
          [inst : CommSemiring R] →
            [inst_1 : CommSemiring S] →
              [inst_2 : CommSemiring A] →
                [inst_3 : CommSemiring B] →
                  [inst_4 : Algebra R S] →
                    [inst_5 : Algebra R A] →
                      [inst_6 : Algebra R B] →
                        [inst_7 : Algebra S A] →
                          [inst_8 : IsScalarTower R S A] →
                            [inst_9 : AddCommMonoid M] →
                              TensorProduct R A (AddMonoidAlgebra B M) ≃ₐ[S] AddMonoidAlgebra (TensorProduct R A B) M

The base change of B[M] to an R-algebra A is isomorphic to (A ⊗[R] B)[M] as an A-algebra.

Defined in

Mathlib.RingTheory.TensorProduct.MonoidAlgebra

Cited by

4 results in Mathlib

Foundations

Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringCommSemiringCommSemiringCommSemiringAlgebraAlgebraAlgebraAlgebraIsScalarTowerAddCommMonoid