Theorems · Definition · commutative algebra
Ideal.toCotangent
{R : Type u} → [inst : CommRing R] → (I : Ideal R) → ↥I →ₗ[R] I.CotangentThe quotient map from I to I ⧸ I ^ 2.
- Defined in
- Mathlib.RingTheory.Ideal.Cotangent
- Cited by
- 45 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- LinearMapstatement · cited by 10,215
- Top.topproof · cited by 9,680
- Idealstatement and proof · cited by 4,748
- Submodule.mkQproof · cited by 232
- Ideal.Cotangentstatement · cited by 68
Cited by49
Results whose statement or proof uses this declaration.
- Algebra.Extension.Cotangent.mkproof · cited by 49
- Ideal.toCotangent_surjectivestatement · cited by 15
- Algebra.Generators.Cotangent.exactproof · cited by 6
- Ideal.Cotangent.equivOfEqproof · cited by 4
- Ideal.tensorCotangentHomproof · cited by 3
- Ideal.toCotangent_eq_zerostatement · cited by 3
- Ideal.toCotangent_rangestatement · cited by 3
- Ideal.cotangent_subsingleton_iffproof · cited by 3
- KaehlerDifferential.tensorProductTo_surjectiveproof · cited by 3
- Ideal.mem_toCotangent_kerstatement and proof · cited by 2
- KaehlerDifferential.fromIdealproof · cited by 2
- Ideal.Cotangent.smul_eq_zero_of_memproof · cited by 2