Theorems · Theorem · commutative algebra

Algebra.FormallyUnramified.lift_unique_of_ringHom

∀ {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] {C : Type u_1} [inst_6 : Ring C]
  (f : B →+* C), IsNilpotent (RingHom.ker f) → ∀ (g₁ g₂ : A →ₐ[R] B), f.comp ↑g₁ = f.comp ↑g₂ → g₁ = g₂

Defined in

Mathlib.RingTheory.Unramified.Basic

Cited by

1 results in Mathlib

Foundations

Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraCommRingAlgebraAlgebra.FormallyUnramifiedRing