Theorems · Theorem · commutative algebra
IsLocalRing.maximalIdeal_height_eq_ringKrullDim
∀ {R : Type u_1} [inst : CommRing R] [inst_1 : IsLocalRing R], ↑(IsLocalRing.maximalIdeal R).height = ringKrullDim RThe height of the maximal ideal equals the Krull dimension in a local ring.
- Defined in
- Mathlib.RingTheory.Ideal.Height
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingIsLocalRing
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 and proof · cited by 4,985
- WithBotstatement · cited by 1,498
- WithBot.somestatement and proof · cited by 541
- IsLocalRingstatement and proof · cited by 339
- IsLocalRing.maximalIdealstatement and proof · cited by 297
- Ideal.heightstatement · cited by 83
- ringKrullDimstatement and proof · cited by 75
- Order.height_top_eq_krullDimproof · cited by 6
Cited by4
Results whose statement or proof uses this declaration.
- IsLocalization.AtPrime.ringKrullDim_eq_heightproof · cited by 4
- ringKrullDim_le_spanFinrank_maximalIdealproof · cited by 1
- Ideal.height_eq_ringKrullDim_iffproof · cited by 0