Theorems · Definition · commutative algebra

KaehlerDifferential.derivationTensorProduct

(R : Type u_1) →
  (S : Type u_2) →
    (A : Type u_3) →
      (B : Type u_4) →
        [inst : CommRing R] →
          [inst_1 : CommRing S] →
            [inst_2 : Algebra R S] →
              [inst_3 : CommRing A] →
                [inst_4 : CommRing B] →
                  [inst_5 : Algebra R A] →
                    [inst_6 : Algebra R B] →
                      [inst_7 : Algebra A B] →
                        [inst_8 : Algebra S B] →
                          [inst_9 : IsScalarTower R A B] →
                            [inst_10 : IsScalarTower R S B] →
                              [h : Algebra.IsPushout R S A B] → Derivation S B (TensorProduct R S Ω[A⁄R])

(Implementation). The S-derivation B = S ⊗[R] A to S ⊗[R] Ω[A⁄R] sending a ⊗ b to a ⊗ d b.

Defined in

Mathlib.RingTheory.Kaehler.TensorProduct

Cited by

3 results in Mathlib

Foundations

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

Assumes

CommRingCommRingAlgebraCommRingCommRingAlgebraAlgebraAlgebraAlgebraIsScalarTowerIsScalarTowerAlgebra.IsPushout