Theorems · Theorem · commutative algebra
IsLocalRing.finrank_cotangentSpace_eq_zero_iff
∀ {R : Type u_1} [inst : CommRing R] [inst_1 : IsLocalRing R] [IsNoetherianRing R],
Module.finrank (IsLocalRing.ResidueField R) (IsLocalRing.CotangentSpace R) = 0 ↔ IsField R- Defined in
- Mathlib.RingTheory.Ideal.Cotangent
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 130 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Module.finrankstatement · cited by 1,770
- IsLocalRingstatement and proof · cited by 339
- IsLocalRing.maximalIdealstatement · cited by 297
- IsNoetherianRingstatement and proof · cited by 268
- IsLocalRing.ResidueFieldstatement · cited by 156
- IsFieldstatement and proof · cited by 103
- IsLocalRing.CotangentSpacestatement · cited by 16
- Module.finrank_zero_iffproof · cited by 6
- IsLocalRing.subsingleton_cotangentSpace_iffproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- IsLocalRing.finrank_cotangentSpace_eq_zeroproof · cited by 1