Theorems · Definition · commutative algebra

KaehlerDifferential.linearMapEquivDerivation

(R : Type u) →
  (S : Type v) →
    [inst : CommRing R] →
      [inst_1 : CommRing S] →
        [inst_2 : Algebra R S] →
          {M : Type u_1} →
            [inst_3 : AddCommGroup M] →
              [inst_4 : Module R M] →
                [inst_5 : Module S M] → [inst_6 : IsScalarTower R S M] → (Ω[S⁄R] →ₗ[S] M) ≃ₗ[S] Derivation R S M

The S-linear maps from Ω[S⁄R] to M are (S-linearly) equivalent to R-derivations from S to M.

Defined in

Mathlib.RingTheory.Kaehler.Basic

Cited by

3 results in Mathlib

Foundations

Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraAddCommGroupModuleModuleIsScalarTower