Theorems · Definition · ring theory

MonoidAlgebra.lift

(R : Type u_1) →
  (A : Type u_4) →
    (M : Type u_7) →
      [inst : CommSemiring R] →
        [inst_1 : Semiring A] → [inst_2 : Algebra R A] → [inst_3 : Monoid M] → (M →* A) ≃ (MonoidAlgebra R M →ₐ[R] A)

Any monoid homomorphism M →* A can be lifted to an algebra homomorphism R[M] →ₐ[R] A.

Defined in

Mathlib.Algebra.MonoidAlgebra.Basic

Cited by

13 results in Mathlib

Foundations

Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringSemiringAlgebraMonoid