Theorems · Theorem · commutative algebra
Ideal.eq_of_le_of_height_le
∀ {R : Type u_1} [inst : CommRing R] (I : Ideal R) [I.IsPrime] [I.FiniteHeight] {J : Ideal R},
I ≤ J → J.height ≤ I.height → I = JA prime ideal of finite height is equal to any ideal that contains it with no greater height.
- Defined in
- Mathlib.RingTheory.Ideal.Height
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Ideal.IsPrimestatement and proof · cited by 827
- not_leproof · cited by 328
- Ideal.heightstatement and proof · cited by 83
- eq_of_le_of_not_ltproof · cited by 28
- Ideal.FiniteHeightstatement and proof · cited by 18
- Ideal.height_strict_mono_of_isPrimeproof · cited by 4
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.