Theorems · Theorem · commutative algebra

KaehlerDifferential.tensorKaehlerEquivBase_tmul

∀ (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]
  [inst_11 : Algebra.IsPushout R S A B] (a : S) (b : Ω[A⁄R]),
  (KaehlerDifferential.tensorKaehlerEquivBase R S A B) (a ⊗ₜ[R] b) = a • (KaehlerDifferential.map R S A B) b

Defined in

Mathlib.RingTheory.Kaehler.TensorProduct

Cited by

3 results in Mathlib

Foundations

Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraCommRingCommRingAlgebraAlgebraAlgebraAlgebraIsScalarTowerIsScalarTowerAlgebra.IsPushout