Theorems · Definition · ring theory

LinearMap.smulRight

{R : Type u_1} →
  {S : Type u_3} →
    {M : Type u_4} →
      {M₁ : Type u_5} →
        [inst : Semiring R] →
          [inst_1 : AddCommMonoid M] →
            [inst_2 : AddCommMonoid M₁] →
              [inst_3 : Module R M] →
                [inst_4 : Module R M₁] →
                  [inst_5 : Semiring S] →
                    [inst_6 : Module R S] →
                      [inst_7 : Module S M] → [IsScalarTower R S M] → (M₁ →ₗ[R] S) → M → M₁ →ₗ[R] M

When f is an R-linear map taking values in S, then fun b ↦ f b • x is an R-linear map.

Defined in

Mathlib.Algebra.Module.LinearMap.End

Cited by

54 results in Mathlib

Foundations

Depth 24 from the axioms · uses no axioms

Assumes

SemiringAddCommMonoidAddCommMonoidModuleModuleSemiringModuleModuleIsScalarTower