Theorems · Theorem · commutative algebra

Algebra.FormallyUnramified.iff_comp_injective

∀ {R : Type v} [inst : CommRing R] {A : Type u} [inst_1 : CommRing A] [inst_2 : Algebra R A],
  Algebra.FormallyUnramified R A ↔
    ∀ ⦃B : Type u⦄ [inst_3 : CommRing B] [inst_4 : Algebra R B] (I : Ideal B),
      I ^ 2 = ⊥ → Function.Injective (Ideal.Quotient.mkₐ R I).comp

A version without stray universes that is more easy to rewrite with.

Defined in

Mathlib.RingTheory.Unramified.Basic

Cited by

8 results in Mathlib

Foundations

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

Assumes

CommRingCommRingAlgebra