Theorems · Theorem · commutative algebra
isRegularLocalRing_iff
∀ (R : Type u_1) [inst : CommRing R] [inst_1 : IsLocalRing R] [IsNoetherianRing R], IsRegularLocalRing R ↔ ↑(Submodule.spanFinrank (IsLocalRing.maximalIdeal R)) = ringKrullDim R
- Defined in
- Mathlib.RingTheory.RegularLocalRing.Defs
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- 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 and proof · cited by 8
Cited by4
Results whose statement or proof uses this declaration.
- IsRegularLocalRing.of_ringEquivproof · cited by 2
- IsRegularLocalRing.of_spanFinrank_maximalIdeal_leproof · cited by 1
- IsRegularLocalRing.iff_finrank_cotangentSpaceproof · cited by 0