Theorems · Theorem · commutative algebra
Ideal.exists_ltSeries_length_eq_height
∀ {R : Type u_1} [inst : CommRing R] (p : Ideal R) [inst_1 : p.IsPrime] [p.FiniteHeight],
∃ l, RelSeries.last l = { asIdeal := p, isPrime := ⋯ } ∧ ↑l.length = p.height- Defined in
- Mathlib.RingTheory.Ideal.Height
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- Set.ofPredstatement · cited by 6,101
- ENatstatement and proof · cited by 4,985
- Idealstatement and proof · cited by 4,748
- Ideal.IsPrimestatement and proof · cited by 827
- PrimeSpectrumstatement and proof · cited by 625
- RelSeries.lengthstatement and proof · cited by 195
- RelSeries.laststatement and proof · cited by 114
- LTSeriesstatement and proof · cited by 87
- Ideal.heightstatement and proof · cited by 83
- Ideal.IsPrime.ne_topproof · cited by 82
- Ideal.FiniteHeightstatement and proof · cited by 18
Cited by1
Results whose statement or proof uses this declaration.
- Ideal.height_eq_height_add_of_liesOver_of_hasGoingDownproof · cited by 1