Theorems · Theorem · commutative algebra
Ideal.height_le_height_add_spanFinrank_of_le
∀ {R : Type u_1} [inst : CommRing R] [IsNoetherianRing R] {I p : Ideal R} [p.IsPrime],
I ≤ p → p.height ≤ (Ideal.map (Ideal.Quotient.mk I) p).height + ↑(Submodule.spanFinrank I)If I ≤ p and p is prime, the height of p is bounded by the height of p ⧸ I R plus
the span rank of I.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 146 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites53
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- Set.imageproof · cited by 5,609
- ENatstatement · cited by 4,985
- Idealstatement and proof · cited by 4,748
Cited by2
Results whose statement or proof uses this declaration.
- height_le_ringKrullDim_quotient_add_spanFinrankproof · cited by 2
- Ideal.height_le_height_add_encard_of_subsetproof · cited by 1