Theorems · Theorem · commutative algebra
Ideal.exists_spanRank_eq_and_height_eq
∀ {R : Type u_1} [inst : CommRing R] [IsNoetherianRing R] (I : Ideal R),
I ≠ ⊤ → ∃ J ≤ I, Submodule.spanRank J = ↑I.height ∧ J.height = I.height- Cited by
- 1 results in Mathlib
- Foundations
- Depth 143 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingIsNoetherianRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
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
- Top.topstatement and proof · cited by 9,680
- ENatstatement and proof · cited by 4,985
- Idealstatement and proof · cited by 4,748
- Cardinalstatement and proof · cited by 2,598
- le_antisymmproof · cited by 2,068
- le_transproof · cited by 985
- IsNoetherianRingstatement and proof · cited by 268
- top_le_iffproof · cited by 175
- ENat.toNatproof · cited by 143
- Ideal.heightstatement and proof · cited by 83
- Cardinal.ofENatstatement and proof · cited by 66
Cited by1
Results whose statement or proof uses this declaration.
- Ideal.height_le_iff_exists_minimalPrimesproof · cited by 1