algebraLid — Mathlib

English

Under suitable localization hypotheses, the pushout of rings with respect to T → B and R → A coincides with the localization of B by the submonoid Algebra.algebraMapSubmonoid T S.

Русский

При условиях локализации, объединение колец через таврки просходит через локализацию B по подмножество моноида.

LaTeX

$$Algebra.IsPushout R T A B$$

Lean4

/-- If `A` is a localization of `R`, tensoring an `A`-algebra with `A` over `R` does nothing. -/
noncomputable def algebraLid : A ⊗[R] B ≃ₐ[A] B :=
  have := tensorProduct_compatibleSMul S A A B
  Algebra.TensorProduct.lidOfCompatibleSMul R A B

Похожие утверждения