Theorems · Definition · ring theory

AddMonoidAlgebra.domCongr

(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] → M ≃+ N → AddMonoidAlgebra A M ≃ₐ[R] AddMonoidAlgebra A N

If e : M ≃+ N is an additive equivalence between two additive monoids, then AddMonoidAlgebra.domCongr e is an algebra equivalence between their additive monoid algebras.

Defined in

Mathlib.Algebra.MonoidAlgebra.Basic

Cited by

21 results in Mathlib

Foundations

Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringSemiringAlgebraAddMonoidAddMonoid