Theorems · Theorem · commutative algebra
Ring.HasFiniteQuotients.finite_cardQuot_heightOneSpectrum_le
∀ {R : Type u_1} [inst : CommRing R] [Ring.HasFiniteQuotients R] (B : ℕ), {p | Submodule.cardQuot p.asIdeal ≤ B}.FiniteA ring with finite quotients has only finitely many nonzero prime ideals of bounded norm.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Set.Finitestatement · cited by 1,814
- IsDedekindDomain.HeightOneSpectrumstatement and proof · cited by 338
- Function.Injective.injOnproof · cited by 280
- IsDedekindDomain.HeightOneSpectrum.asIdealstatement · cited by 156
- Ring.HasFiniteQuotientsstatement and proof · cited by 19
- Submodule.cardQuotstatement · cited by 14
- Set.Finite.of_injOnproof · cited by 7
- IsDedekindDomain.HeightOneSpectrum.extproof · cited by 7
- Ring.HasFiniteQuotients.finite_cardQuot_leproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Ring.HasFiniteQuotients.finite_absNorm_heightOneSpectrum_leproof · cited by 0