Theorems · Theorem · commutative algebra

Algebra.FormallySmooth.liftOfSurjective_apply

∀ {R : Type u} {A : Type v} [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : Algebra R A] {B : Type u_1}
  [inst_3 : CommRing B] [inst_4 : Algebra R B] {C : Type u_4} [inst_5 : CommRing C] [inst_6 : Algebra R C]
  [inst_7 : Algebra.FormallySmooth R A] (f : A →ₐ[R] C) (g : B →ₐ[R] C) (hg : Function.Surjective ⇑g)
  (hg' : IsNilpotent (RingHom.ker g)) (x : A), g ((Algebra.FormallySmooth.liftOfSurjective f g hg hg') x) = f x

Defined in

Mathlib.RingTheory.Smooth.Basic

Cited by

1 results in Mathlib

Foundations

Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraCommRingAlgebraCommRingAlgebraAlgebra.FormallySmooth