Theorems · Definition · commutative algebra

KaehlerDifferential.kerToTensor

(R : Type u) →
  [inst : CommRing R] →
    (A : Type u_2) →
      (B : Type u_3) →
        [inst_1 : CommRing A] →
          [inst_2 : CommRing B] →
            [inst_3 : Algebra R A] →
              [inst_4 : Algebra A B] → ↥(RingHom.ker (algebraMap A B)) →ₗ[A] TensorProduct A B Ω[A⁄R]

The map I → B ⊗[A] Ω[A⁄R] where I = ker(A → B).

Defined in

Mathlib.RingTheory.Kaehler.Basic

Cited by

11 results in Mathlib

Foundations

Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingCommRingAlgebraAlgebra