Theorems · Definition · ring theory

MonoidAlgebra.mapDomainAlgHom

(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 : Monoid M] → [inst_4 : Monoid N] → (M →* N) → MonoidAlgebra A M →ₐ[R] MonoidAlgebra A N

If f : M → N is a monoid homomorphism, then MonoidAlgebra.mapDomain f is an algebra homomorphism between their monoid algebras.

Defined in

Mathlib.Algebra.MonoidAlgebra.Basic

Cited by

4 results in Mathlib

Foundations

Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringSemiringAlgebraMonoidMonoid