Theorems · Theorem · commutative algebra

Algebra.FormallyUnramified.lift_unique

∀ {R : Type v} [inst : CommRing R] {A : Type u} [inst_1 : CommRing A] [inst_2 : Algebra R A] {B : Type w}
  [inst_3 : CommRing B] [inst_4 : Algebra R B] [Algebra.FormallyUnramified R A] (I : Ideal B),
  IsNilpotent I → ∀ (g₁ g₂ : A →ₐ[R] B), (Ideal.Quotient.mkₐ R I).comp g₁ = (Ideal.Quotient.mkₐ R I).comp g₂ → g₁ = g₂

Defined in

Mathlib.RingTheory.Unramified.Basic

Cited by

3 results in Mathlib

Foundations

Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraCommRingAlgebraAlgebra.FormallyUnramified