Theorems · Theorem · commutative algebra
Ideal.height_strict_mono_of_isPrime_of_isPrime
∀ {R : Type u_1} [inst : CommRing R] {I J : Ideal R} [I.IsPrime] [J.IsPrime],
I < J → ∀ [J.FiniteHeight], I.height < J.height- Defined in
- Mathlib.RingTheory.Ideal.Height
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- LT.lt.leproof · cited by 2,189
- LT.lt.neproof · cited by 872
- Ideal.IsPrimestatement and proof · cited by 827
- lt_of_le_of_ltproof · cited by 432
- Ideal.heightstatement · cited by 83
- Ideal.IsPrime.ne_top'proof · cited by 38
- Ideal.FiniteHeightstatement and proof · cited by 18
- Ideal.height_monoproof · cited by 10
- Ideal.height_lt_topproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- Ideal.eq_span_singleton_of_height_eq_oneproof · cited by 2
- Ideal.mem_minimalPrimes_span_of_mem_minimalPrimes_span_insertproof · cited by 1
- Ideal.height_strict_mono_of_isPrime_of_is_primeproof · cited by 0