Theorems · Theorem · commutative algebra
Ideal.exists_finset_card_eq_height_of_isNoetherianRing
∀ {R : Type u_1} [inst : CommRing R] [IsNoetherianRing R] (p : Ideal R) [p.IsPrime],
∃ s, p ∈ (Ideal.span ↑s).minimalPrimes ∧ ↑s.card = p.heightIf p is a prime in a Noetherian ring R, there exists a p-primary ideal I
spanned by p.height elements.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 145 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites34
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Finsetstatement · cited by 13,712
- SetLike.coestatement · cited by 8,199
- Submoduleproof · cited by 7,192
- ENatstatement and proof · cited by 4,985
- Idealstatement and proof · cited by 4,748
- Cardinalproof · cited by 2,598
- Finset.cardstatement · cited by 2,327
- le_antisymmproof · cited by 2,068
- Set.Finiteproof · cited by 1,814
Cited by2
Results whose statement or proof uses this declaration.
- Ideal.height_le_height_add_spanFinrank_of_leproof · cited by 2
- Ideal.height_le_height_add_of_liesOverproof · cited by 1