Theorems · Definition · commutative algebra
Ideal.height
{R : Type u_1} → [inst : CommRing R] → Ideal R → ℕ∞The height of an ideal is defined as the infimum of the heights of its minimal prime ideals.
- Defined in
- Mathlib.RingTheory.Ideal.Height
- Cited by
- 83 results in Mathlib
- Foundations
- Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Idealstatement and proof · cited by 4,748
- iInfproof · cited by 1,690
- Ideal.minimalPrimesproof · cited by 74
Cited by85
Results whose statement or proof uses this declaration.
- Ideal.height_monostatement · cited by 10
- Ideal.height_eq_inf_minimalPrimesstatement · cited by 7
- IsLocalization.height_understatement and proof · cited by 6
- Ideal.height_eq_zero_iffstatement · cited by 5
- Ideal.height_le_ringKrullDim_of_ne_topstatement · cited by 5
- Ideal.height_le_spanRank_toENat_of_mem_minimalPrimesstatement and proof · cited by 5
- Ideal.height_ne_topstatement · cited by 5
- Ideal.height_botstatement · cited by 4
- Ideal.height_le_one_of_isPrincipal_of_mem_minimalPrimesstatement and proof · cited by 4
- Ideal.height_lt_topstatement · cited by 4
- Ideal.height_strict_mono_of_isPrimestatement and proof · cited by 4
- Ideal.height_topstatement · cited by 4