Theorems · Definition · ring theory

AddMonoidAlgebra.mapDomainNonUnitalAlgHom

(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 : Add M] → [inst_4 : Add N] → (M →ₙ+ N) → AddMonoidAlgebra A M →ₙₐ[R] AddMonoidAlgebra A N

If f : M → N is a homomorphism between two additive magmas, then AddMonoidAlgebra.mapDomain f is a non-unital algebra homomorphism between their additive magma algebras.

Defined in

Mathlib.Algebra.MonoidAlgebra.Basic

Cited by

1 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringSemiringAlgebraAddAdd