Theorems · Theorem · commutative algebra

Algebra.FormallySmooth.localization_map

∀ {R : Type u_4} {A : Type u_5} {Rₘ : Type u_6} {Sₘ : Type u_7} [inst : CommRing R] [inst_1 : CommRing A]
  [inst_2 : CommRing Rₘ] [inst_3 : CommRing Sₘ] (M : Submonoid R) [inst_4 : Algebra R A] [inst_5 : Algebra R Sₘ]
  [inst_6 : Algebra A Sₘ] [inst_7 : Algebra R Rₘ] [inst_8 : Algebra Rₘ Sₘ] [IsScalarTower R Rₘ Sₘ]
  [IsScalarTower R A Sₘ] [IsLocalization M Rₘ] [IsLocalization (Submonoid.map (algebraMap R A) M) Sₘ]
  [Algebra.FormallySmooth R A], Algebra.FormallySmooth Rₘ Sₘ

Defined in

Mathlib.RingTheory.Smooth.Basic

Cited by

0 results in Mathlib

Foundations

Depth 131 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingCommRingCommRingAlgebraAlgebraAlgebraAlgebraAlgebraIsScalarTowerIsScalarTowerIsLocalizationIsLocalizationAlgebra.FormallySmooth