Theorems · Theorem · commutative algebra
IsLocalRing.finrank_CotangentSpace_eq_one_iff
∀ {R : Type u_1} [inst : CommRing R] [IsNoetherianRing R] [inst_2 : IsLocalRing R] [inst_3 : IsDomain R],
Module.finrank (IsLocalRing.ResidueField R) (IsLocalRing.CotangentSpace R) = 1 ↔ IsDiscreteValuationRing R- Cited by
- 1 results in Mathlib
- Foundations
- Depth 134 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
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
- Fieldproof · cited by 7,404
- Idealproof · cited by 4,748
- Bot.botproof · cited by 4,720
- IsDomainstatement and proof · cited by 2,196
- Module.finrankstatement and proof · cited by 1,770
- Ideal.IsPrimeproof · cited by 827
- IsDedekindDomainproof · cited by 668
- IsLocalRingstatement and proof · cited by 339
- IsLocalRing.maximalIdealstatement and proof · cited by 297
- ExistsUniqueproof · cited by 268
- IsNoetherianRingstatement and proof · cited by 268
Cited by1
Results whose statement or proof uses this declaration.
- IsLocalRing.finrank_CotangentSpace_eq_oneproof · cited by 0