Theorems · Theorem · commutative algebra

Ideal.mapCotangent_surjective_of_comap_eq

∀ {A : Type u_1} {B : Type u_2} [inst : CommRing A] [inst_1 : CommRing B] [inst_2 : Algebra A B],
  Function.Surjective ⇑(algebraMap A B) →
    ∀ {I : Ideal B} {J : Ideal A} (eq : Ideal.comap (algebraMap A B) I = RingHom.ker (algebraMap A B) ⊔ J),
      Function.Surjective ⇑(J.mapCotangent I (Algebra.ofId A B) ⋯)

Defined in

Mathlib.RingTheory.Ideal.Cotangent

Cited by

1 results in Mathlib

Foundations

Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebra