algebra_localization_localization

English

A construction of an algebra that encodes the tower of localizations between S_p and T_p via a prime localization of R.

Русский

Конструкция алгебры, кодирующая каскад локализаций между S_p и T_p через локализацию R по простому идеалу.

LaTeX

$$$\text{algebra_localization_localization}$$$

Lean4

/-- Let `R ⊆ S ⊆ T` be a tower of rings. Let `Sₚ` and `Tₚ` denote the localizations of `S` and `T` at
the prime ideal `P` of `R`. Then `Tₚ` is a `Sₚ`-algebra.
This cannot be an instance since it creates a diamond when `S = T`.
-/
noncomputable abbrev algebra_localization_localization : Algebra Sₚ Tₚ :=
  localizationAlgebra P' T

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