Theorems · Theorem · commutative algebra

IsLocalRing.finrank_CotangentSpace_eq_one

∀ (R : Type u_1) [inst : CommRing R] [inst_1 : IsDomain R] [inst_2 : IsDiscreteValuationRing R],
  Module.finrank (IsLocalRing.ResidueField R) (IsLocalRing.CotangentSpace R) = 1

Defined in: Mathlib.RingTheory.DiscreteValuationRing.TFAE
Cited by: 0 results in Mathlib
Foundations: Depth 135 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing IsDomain IsDiscreteValuationRing

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CommRingstatement and proof · cited by 17,173
IsDomainstatement and proof · cited by 2,196
Module.finrankstatement · cited by 1,770
IsLocalRing.maximalIdealstatement · cited by 297
IsLocalRing.ResidueFieldstatement · cited by 156
IsDiscreteValuationRingstatement and proof · cited by 117
IsLocalRing.CotangentSpacestatement · cited by 16
IsLocalRing.finrank_CotangentSpace_eq_one_iffproof · cited by 1

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