Theorems · Definition · commutative algebra

KaehlerDifferential.quotientCotangentIdealRingEquiv

(R : Type u) →
  (S : Type v) →
    [inst : CommRing R] →
      [inst_1 : CommRing S] →
        [inst_2 : Algebra R S] →
          (TensorProduct R S S ⧸ KaehlerDifferential.ideal R S ^ 2) ⧸ (KaehlerDifferential.ideal R S).cotangentIdeal ≃+*
            S

The quotient ring of S ⊗ S ⧸ J ^ 2 by Ω[S⁄R] is isomorphic to S.

Defined in

Mathlib.RingTheory.Kaehler.Basic

Cited by

1 results in Mathlib

Foundations

Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebra