Theorems · Definition · ring theory

LinearMap.mulLeft

(R : Type u_14) →
  {A : Type u_15} →
    [inst : Semiring R] →
      [inst_1 : NonUnitalNonAssocSemiring A] → [inst_2 : Module R A] → [SMulCommClass R A A] → A → A →ₗ[R] A

The multiplication on the left in an algebra is a linear map. Note that this only assumes SMulCommClass R A A, so that it also works for R := Aᵐᵒᵖ. When A is unital and associative, this is the same as DistribSMul.toLinearMap R A a

Defined in

Mathlib.Algebra.Module.LinearMap.Defs

Cited by

34 results in Mathlib

Foundations

Depth 17 from the axioms · uses no axioms

Assumes

SemiringNonUnitalNonAssocSemiringModuleSMulCommClass