Theorems · Definition · commutative algebra

Derivation.tensorProductTo

{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] → [IsScalarTower R S M] → Derivation R S M → TensorProduct R S S →ₗ[S] M

For an R-derivation S → M, this is the map S ⊗[R] S →ₗ[S] M sending s ⊗ₜ t ↦ s • D t.

Defined in

Mathlib.RingTheory.Kaehler.Basic

Cited by

10 results in Mathlib

Foundations

Depth 60 from the axioms · uses propext, Quot.sound

Assumes

CommRingCommRingAlgebraAddCommGroupModuleModuleIsScalarTower