Theorems · Definition · commutative algebra

Ideal.mapCotangent

{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) → I₁ ≤ Ideal.comap f I₂ → I₁.Cotangent →ₗ[R] I₂.Cotangent

The map I/I² → J/J² if I ≤ f⁻¹(J).

Defined in

Mathlib.RingTheory.Ideal.Cotangent

Cited by

6 results in Mathlib

Foundations

Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingCommRingAlgebraAlgebra