Theorems · Theorem · commutative algebra

Algebra.FormallySmooth.of_restrictScalars

∀ (R : Type u_4) [inst : CommRing R] (A : Type u_5) [inst_1 : CommRing A] [inst_2 : Algebra R A] (B : Type u_6)
  [inst_3 : CommRing B] [inst_4 : Algebra R B] [inst_5 : Algebra A B] [IsScalarTower R A B]
  [Algebra.FormallyUnramified R A] [Algebra.FormallySmooth R B], Algebra.FormallySmooth A B

Defined in

Mathlib.RingTheory.Smooth.Basic

Cited by

2 results in Mathlib

Foundations

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

Assumes

CommRingCommRingAlgebraCommRingAlgebraAlgebraIsScalarTowerAlgebra.FormallyUnramifiedAlgebra.FormallySmooth