Theorems · Theorem · ring theory

AddMonoidAlgebra.liftMagma_apply_apply

∀ (R : Type u_1) {A : Type u_4} {M : Type u_7} [inst : Semiring R] [inst_1 : Add M]
  [inst_2 : NonUnitalNonAssocSemiring A] [inst_3 : Module R A] [inst_4 : IsScalarTower R A A]
  [inst_5 : SMulCommClass R A A] (f : Multiplicative M →ₙ* A) (a : AddMonoidAlgebra R M),
  ((AddMonoidAlgebra.liftMagma R) f) a =
    (↑((Finsupp.liftAddHom fun x => (smulAddHom R A).flip (f (Multiplicative.ofAdd x))).comp
            AddMonoidAlgebra.coeffAddEquiv.toAddMonoidHom)).toFun
      a

Defined in

Mathlib.Algebra.MonoidAlgebra.Basic

Cited by

0 results in Mathlib

Foundations

Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddNonUnitalNonAssocSemiringModuleIsScalarTowerSMulCommClass