Theorems · Theorem · commutative algebra
Ideal.height_mono
∀ {R : Type u_1} [inst : CommRing R] {I J : Ideal R}, I ≤ J → I.height ≤ J.height- Defined in
- Mathlib.RingTheory.Ideal.Height
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 71 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.
Cites13
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
- LE.le.transproof · cited by 3,151
- Ideal.IsPrimeproof · cited by 827
- Ideal.heightstatement · cited by 83
- Ideal.minimalPrimesproof · cited by 74
- le_iInf₂proof · cited by 67
- iInf₂_leproof · cited by 45
- Ideal.IsMinimalPrime.isPrimeproof · cited by 26
- Ideal.IsMinimalPrime.leproof · cited by 23
- Ideal.exists_minimalPrimes_leproof · cited by 14
Cited by10
Results whose statement or proof uses this declaration.
- Ideal.mem_minimalPrimes_of_height_leproof · cited by 3
- Ideal.height_strict_mono_of_isPrime_of_isPrimeproof · cited by 3
- ringKrullDim_le_iff_isMaximal_height_leproof · cited by 2
- Ideal.finiteHeight_of_leproof · cited by 1
- Ideal.sup_isMaximal_height_eq_ringKrullDimproof · cited by 1
- Ideal.height_span_singleton_le_oneproof · cited by 1
- exists_spanRank_le_and_le_height_of_le_heightproof · cited by 1
- Ideal.exists_spanRank_eq_and_height_eqproof · cited by 1
- Ideal.height_le_iff_covByproof · cited by 0
- Ideal.exists_isMaximal_heightproof · cited by 0