toModuleEnd — Mathlib

English

If f' is injective, then f'^n is injective for all n.

Русский

Если f' инъективен, то f'^n инъективен для всех n.

LaTeX

$$$\\forall n,\\; \\text{Injective}(f'^n).$$$

Lean4

/-- Each element of the monoid defines a module endomorphism.

This is a stronger version of `DistribMulAction.toAddMonoidEnd`. -/
@[simps]
def toModuleEnd : S →* Module.End R M where
  toFun := toLinearMap R M
  map_one' := LinearMap.ext <| one_smul _
  map_mul' _ _ := LinearMap.ext <| mul_smul _ _

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