Theorems · Theorem · commutative algebra
Derivation.tensorProductTo_tmul
∀ {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]
(D : Derivation R S M) (s t : S), D.tensorProductTo (s ⊗ₜ[R] t) = s • D t- Defined in
- Mathlib.RingTheory.Kaehler.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- Algebrastatement and proof · cited by 11,388
- LinearMapstatement · cited by 10,215
- IsScalarTowerstatement and proof · cited by 3,896
- TensorProductstatement · cited by 2,545
- TensorProduct.tmulstatement · cited by 1,182
- Derivationstatement and proof · cited by 293
- Derivation.tensorProductTostatement · cited by 10
Cited by1
Results whose statement or proof uses this declaration.
- Derivation.liftKaehlerDifferential_compproof · cited by 6