Theorems · Theorem · commutative algebra
IsRegularLocalRing.of_spanFinrank_maximalIdeal_le
∀ (R : Type u_1) [inst : CommRing R] [inst_1 : IsLocalRing R] [IsNoetherianRing R], ↑(Submodule.spanFinrank (IsLocalRing.maximalIdeal R)) ≤ ringKrullDim R → IsRegularLocalRing R
- Defined in
- Mathlib.RingTheory.RegularLocalRing.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 143 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- le_antisymmproof · cited by 2,068
- WithBotstatement · cited by 1,498
- IsLocalRingstatement and proof · cited by 339
- IsLocalRing.maximalIdealstatement and proof · cited by 297
- IsNoetherianRingstatement and proof · cited by 268
- ringKrullDimstatement and proof · cited by 75
- Submodule.spanFinrankstatement and proof · cited by 49
- IsRegularLocalRingstatement · cited by 8
- isRegularLocalRing_iffproof · cited by 4
- ringKrullDim_le_spanFinrank_maximalIdealproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.