Theorems · Definition · ring theory

AddMonoidAlgebra.commAlgEquiv

(R : Type u_1) →
  {A : Type u_4} →
    {M : Type u_7} →
      {N : Type u_8} →
        [inst : CommSemiring R] →
          [inst_1 : Semiring A] →
            [inst_2 : Algebra R A] →
              [inst_3 : AddMonoid M] →
                [inst_4 : AddMonoid N] →
                  AddMonoidAlgebra (AddMonoidAlgebra A M) N ≃ₐ[R] AddMonoidAlgebra (AddMonoidAlgebra A N) M

Nested monoid algebras can be taken in an arbitrary order.

Defined in

Mathlib.Algebra.MonoidAlgebra.Basic

Cited by

4 results in Mathlib

Foundations

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

Assumes

CommSemiringSemiringAlgebraAddMonoidAddMonoid