localizationAway — Mathlib

English

The jacobian of localizationAway is a unit due to the localization map sending units to units.

Русский

Якобиан локализации является единицей, поскольку локализационная карта отправляет единицы в единицы.

LaTeX

$$$\\operatorname{jacobian}(\\text{localizationAway}(S,r)) = \\text{isUnit}$$$

Lean4

/-- If `S` is the localization of `R` at `r`, this is the canonical submersive presentation
of `S` as `R`-algebra. -/
noncomputable def localizationAway : SubmersivePresentation R S Unit Unit
    where
  __ := PreSubmersivePresentation.localizationAway S r
  jacobian_isUnit := by
    rw [localizationAway_jacobian]
    apply IsLocalization.map_units _ (⟨r, 1, by simp⟩ : Submonoid.powers r)

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