Theorems · Theorem · commutative algebra

KaehlerDifferential.exact_mapBaseChange_map

∀ (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.Exact ⇑(KaehlerDifferential.mapBaseChange R A B) ⇑(KaehlerDifferential.map R A B B)

The sequence B ⊗[A] Ω[A⁄R] → Ω[B⁄R] → Ω[B⁄A] → 0 is exact. Also see KaehlerDifferential.map_surjective.

Defined in

Mathlib.RingTheory.Kaehler.Basic

Cited by

0 results in Mathlib

Foundations

Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingCommRingAlgebraAlgebraAlgebraIsScalarTower