Theorems · Theorem · commutative algebra

Ideal.mapCotangent_toCotangent

∀ {R : Type u} [inst : CommRing R] {A : Type u_1} {B : Type u_2} [inst_1 : CommRing A] [inst_2 : CommRing B]
  [inst_3 : Algebra R A] [inst_4 : Algebra R B] (I₁ : Ideal A) (I₂ : Ideal B) (f : A →ₐ[R] B)
  (h : I₁ ≤ Ideal.comap f I₂) (x : ↥I₁), (I₁.mapCotangent I₂ f h) (I₁.toCotangent x) = I₂.toCotangent ⟨f ↑x, ⋯⟩

Defined in

Mathlib.RingTheory.Ideal.Cotangent

Cited by

0 results in Mathlib

Foundations

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

Assumes

CommRingCommRingCommRingAlgebraAlgebra