Theorems · Theorem · commutative algebra

KaehlerDifferential.ker_map_of_surjective

∀ (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] [inst_5 : Algebra R B] [inst_6 : IsScalarTower R A B],
  Function.Surjective ⇑(algebraMap A B) →
    (KaehlerDifferential.map R R A B).ker =
      Submodule.map (Finsupp.linearCombination A ⇑(KaehlerDifferential.D R A))
        (Finsupp.mapRange.linearMap (Algebra.linearMap A B) ∘ₗ Finsupp.lmapDomain A A ⇑(algebraMap A B)).ker

Defined in

Mathlib.RingTheory.Kaehler.Basic

Cited by

1 results in Mathlib

Foundations

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

Assumes

CommRingCommRingCommRingAlgebraAlgebraAlgebraIsScalarTower