Theorems · Theorem · commutative algebra
Ideal.toCotangent_surjective
∀ {R : Type u} [inst : CommRing R] (I : Ideal R), Function.Surjective ⇑I.toCotangent- Defined in
- Mathlib.RingTheory.Ideal.Cotangent
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 86 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- 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
- Ideal.Cotangentstatement · cited by 68
- Submodule.mkQ_surjectiveproof · cited by 48
- Ideal.toCotangentstatement · cited by 45
Cited by15
Results whose statement or proof uses this declaration.
- Algebra.Extension.Cotangent.mk_surjectiveproof · cited by 22
- KaehlerDifferential.tensorProductTo_surjectiveproof · cited by 3
- Ideal.cotangentToQuotientSquare_injectiveproof · cited by 2
- Ideal.Cotangent.smul_eq_zero_of_memproof · cited by 2
- KaehlerDifferential.fromIdeal_surjectiveproof · cited by 1
- Algebra.FormallyUnramified.of_map_maximalIdealproof · cited by 1
- IsLocalRing.finrank_cotangentSpace_le_one_iffproof · cited by 1
- Ideal.mapCotangent_ker_of_surjectiveproof · cited by 1
- Ideal.mapCotangent_surjective_of_comap_eqproof · cited by 1
- Algebra.FormallySmooth.of_surjective_of_ker_eq_map_of_flatproof · cited by 1
- KaehlerDifferential.range_kerCotangentToTensorproof · cited by 1
- Ideal.tensorCotangentHom_injective_of_flatproof · cited by 0