Theorems · Theorem · commutative algebra
IsRegularLocalRing.iff_finrank_cotangentSpace
∀ (R : Type u_1) [inst : CommRing R] [inst_1 : IsLocalRing R] [IsNoetherianRing R], IsRegularLocalRing R ↔ ↑(Module.finrank (IsLocalRing.ResidueField R) (IsLocalRing.CotangentSpace R)) = ringKrullDim R
- Defined in
- Mathlib.RingTheory.RegularLocalRing.Defs
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 123 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites13
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
- ENatstatement · cited by 4,985
- Module.finrankstatement and proof · cited by 1,770
- WithBotstatement · cited by 1,498
- IsLocalRingstatement and proof · cited by 339
- IsLocalRing.maximalIdealstatement · cited by 297
- IsNoetherianRingstatement and proof · cited by 268
- IsLocalRing.ResidueFieldstatement and proof · cited by 156
- ringKrullDimstatement and proof · cited by 75
- IsLocalRing.CotangentSpacestatement and proof · cited by 16
- IsRegularLocalRingstatement · cited by 8
- isRegularLocalRing_iffproof · cited by 4
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