Theorems · Theorem · commutative algebra

Algebra.FormallySmooth.mk_lift

∀ {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] [inst_5 : Algebra.FormallySmooth R A] (I : Ideal B) (hI : IsNilpotent I)
  (g : A →ₐ[R] B ⧸ I) (x : A), (Ideal.Quotient.mk I) ((Algebra.FormallySmooth.lift I hI g) x) = g x

Defined in

Mathlib.RingTheory.Smooth.Basic

Cited by

2 results in Mathlib

Foundations

Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraCommRingAlgebraAlgebra.FormallySmooth