Theorems · Theorem · ring theory

LinearMap.map_smul

∀ {R : Type u_1} {M : Type u_8} {M₂ : Type u_10} [inst : Semiring R] [inst_1 : AddCommMonoid M]
  [inst_2 : AddCommMonoid M₂] [inst_3 : Module R M] [inst_4 : Module R M₂] (fₗ : M →ₗ[R] M₂) (c : R) (x : M),
  fₗ (c • x) = c • fₗ x

Defined in

Mathlib.Algebra.Module.LinearMap.Defs

Cited by

60 results in Mathlib

Foundations

Depth 22 from the axioms · uses no axioms

Assumes

SemiringAddCommMonoidAddCommMonoidModuleModule