Theorems · Definition · commutative algebra
Ideal.cotangentEquivIdeal
{R : Type u} → [inst : CommRing R] → (I : Ideal R) → I.Cotangent ≃ₗ[R] ↥I.cotangentIdealThe equivalence of the two definitions of I / I ^ 2, either as the quotient of I or the
ideal of R / I ^ 2.
- Defined in
- Mathlib.RingTheory.Ideal.Cotangent
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 94 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.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- RingHom.idstatement and proof · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- LinearMapproof · cited by 10,215
- Equivproof · cited by 8,337
- Idealstatement and proof · cited by 4,748
- LinearEquivstatement · cited by 3,317
- HasQuotient.Quotientstatement and proof · cited by 2,301
- Submodule.restrictScalarsproof · cited by 180
- Equiv.invFunproof · cited by 163
- Equiv.ofBijectiveproof · cited by 70
- Ideal.Cotangentstatement and proof · cited by 68
Cited by5
Results whose statement or proof uses this declaration.
- retractionKerCotangentToTensorEquivSectionproof · cited by 2
- Algebra.Extension.Cotangent.map_sub_mapproof · cited by 1
- KaehlerDifferential.endEquivDerivation'proof · cited by 0
- Ideal.cotangentEquivIdeal_applystatement · cited by 0
- Ideal.cotangentEquivIdeal_symm_applystatement and proof · cited by 0