Theorems · Theorem · ring theory

LinearMap.map_smul_of_tower

∀ {M : Type u_8} {M₂ : Type u_10} [inst : AddCommMonoid M] [inst_1 : AddCommMonoid M₂] {R : Type u_14} {S : Type u_15}
  [inst_2 : Semiring S] [inst_3 : SMul R M] [inst_4 : Module S M] [inst_5 : SMul R M₂] [inst_6 : Module S M₂]
  [LinearMap.CompatibleSMul M M₂ R S] (fₗ : M →ₗ[S] M₂) (c : R) (x : M), fₗ (c • x) = c • fₗ x

Defined in

Mathlib.Algebra.Module.LinearMap.Defs

Cited by

50 results in Mathlib

Foundations

Depth 22 from the axioms · uses no axioms

Assumes

AddCommMonoidAddCommMonoidSemiringSMulModuleSMulModuleLinearMap.CompatibleSMul