Theorems · Definition · commutative algebra
IsLocalRing.CotangentSpace
(R : Type u_1) → [inst : CommRing R] → [IsLocalRing R] → Type u_1
The A ⧸ I-vector space I ⧸ I ^ 2.
- Defined in
- Mathlib.RingTheory.Ideal.Cotangent
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingIsLocalRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- IsLocalRingstatement and proof · cited by 339
- IsLocalRing.maximalIdealproof · cited by 297
- Ideal.Cotangentproof · cited by 68
Cited by16
Results whose statement or proof uses this declaration.
- IsDiscreteValuationRing.TFAEstatement and proof · cited by 3
- IsLocalization.AtPrime.isDiscreteValuationRing_of_dedekind_domainproof · cited by 2
- IsLocalRing.spanFinrank_maximalIdeal_eq_finrank_cotangentSpace_of_fgstatement · cited by 2
- IsLocalRing.finrank_CotangentSpace_eq_one_iffstatement and proof · cited by 1
- IsLocalRing.finrank_cotangentSpace_eq_zerostatement · cited by 1
- IsLocalRing.finrank_cotangentSpace_eq_zero_iffstatement · cited by 1
- IsLocalRing.finrank_cotangentSpace_le_one_iffstatement and proof · cited by 1
- IsLocalRing.rank_cotangentSpace_eq_spanrank_maximalIdeal_of_fgstatement and proof · cited by 1
- isDedekindDomainDvr.of_formallyUnramifiedproof · cited by 1
- IsLocalRing.spanFinrank_maximalIdeal_eq_finrank_cotangentSpacestatement · cited by 1
- tfae_of_isNoetherianRing_of_isLocalRing_of_isDomainstatement and proof · cited by 1
- IsLocalRing.subsingleton_cotangentSpace_iffstatement · cited by 1