Theorems · Theorem · ring theory

MonoidAlgebra.lift_unique

∀ {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] (F : MonoidAlgebra R M →ₐ[R] A) (f : MonoidAlgebra R M),
  F f = f.coeff.sum fun a b => b • F (MonoidAlgebra.single a 1)

Decomposition of a R-algebra homomorphism from R[M] by its values on F (single a 1).

Defined in

Mathlib.Algebra.MonoidAlgebra.Basic

Cited by

0 results in Mathlib

Foundations

Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringSemiringAlgebraMonoid