Theorems · Theorem · commutative algebra
Ring.HasFiniteQuotients.finite_absNorm_le
∀ {R : Type u_1} [inst : CommRing R] [Ring.HasFiniteQuotients R] [inst_2 : IsDedekindDomain R]
[inst_3 : Module.Free ℤ R] (B : ℕ), {I | Ideal.absNorm I ≤ B}.FiniteA ring with finite quotients has only finitely many ideals of bounded norm.
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- Foundations
- Depth 154 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Set.ofPredstatement · cited by 6,101
- Idealstatement · cited by 4,748
- Set.Finitestatement · cited by 1,814
- MonoidWithZeroHomstatement · cited by 704
- IsDedekindDomainstatement and proof · cited by 668
- Module.Freestatement and proof · cited by 597
- Ideal.absNormstatement · cited by 123
- Ring.HasFiniteQuotientsstatement and proof · cited by 19
- Ring.HasFiniteQuotients.finite_cardQuot_leproof · cited by 2
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