Theorems · Theorem · commutative algebra
Ideal.isMaximal_of_height_eq_ringKrullDim
∀ {R : Type u_1} [inst : CommRing R] {I : Ideal R} [I.IsPrime] [FiniteRingKrullDim R],
↑I.height = ringKrullDim R → I.IsMaximal- Defined in
- Mathlib.RingTheory.Ideal.Height
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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
- Top.topproof · cited by 9,680
- ENatstatement · cited by 4,985
- Idealstatement and proof · cited by 4,748
- WithBotstatement · cited by 1,498
- Ideal.IsPrimestatement and proof · cited by 827
- WithBot.somestatement and proof · cited by 541
- Ideal.IsMaximalstatement and proof · cited by 452
- Ideal.heightstatement and proof · cited by 83
- ringKrullDimstatement and proof · cited by 75
- Ideal.exists_le_maximalproof · cited by 47
- Ideal.IsMaximal.ne_topproof · cited by 42
Cited by1
Results whose statement or proof uses this declaration.
- Ideal.height_eq_ringKrullDim_iffproof · cited by 0