Theorems · Theorem · commutative algebra
IsLocalRing.finrank_cotangentSpace_eq_zero
∀ (R : Type u_2) [inst : Field R], Module.finrank (IsLocalRing.ResidueField R) (IsLocalRing.CotangentSpace R) = 0
- Defined in
- Mathlib.RingTheory.Ideal.Cotangent
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 131 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fieldstatement and proof · cited by 7,404
- Module.finrankstatement · cited by 1,770
- IsLocalRing.maximalIdealstatement · cited by 297
- IsLocalRing.ResidueFieldstatement · cited by 156
- Field.toIsFieldproof · cited by 18
- IsLocalRing.CotangentSpacestatement · cited by 16
- IsLocalRing.finrank_cotangentSpace_eq_zero_iffproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- IsLocalRing.finrank_CotangentSpace_eq_one_iffproof · cited by 1