Theorems · Definition · commutative algebra
KaehlerDifferential.fromIdeal
(R : Type u) →
(S : Type v) →
[inst : CommRing R] →
[inst_1 : CommRing S] → [inst_2 : Algebra R S] → ↥(KaehlerDifferential.ideal R S) →ₗ[TensorProduct R S S] Ω[S⁄R]The quotient map I → Ω[S⁄R] with I being the kernel of S ⊗[R] S → S.
- Defined in
- Mathlib.RingTheory.Kaehler.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- LinearMapstatement · cited by 10,215
- Idealstatement · cited by 4,748
- TensorProductstatement · cited by 2,545
- KaehlerDifferentialstatement · cited by 204
- Ideal.toCotangentproof · cited by 45
- KaehlerDifferential.idealstatement and proof · cited by 14
Cited by3
Results whose statement or proof uses this declaration.
- KaehlerDifferential.span_range_derivationproof · cited by 7
- KaehlerDifferential.DLinearMapproof · cited by 1
- KaehlerDifferential.fromIdeal_surjectivestatement · cited by 1