Theorems · Theorem · commutative algebra

Algebra.FormallySmooth.exists_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] [Algebra.FormallySmooth R A] (I : Ideal B),
  IsNilpotent I → ∀ (g : A →ₐ[R] B ⧸ I), ∃ f, (Ideal.Quotient.mkₐ R I).comp f = g

Defined in

Mathlib.RingTheory.Smooth.Basic

Cited by

1 results in Mathlib

Foundations

Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraCommRingAlgebraAlgebra.FormallySmooth