Theorems · Theorem · number theory
IsDedekindDomain.integer_univ
∀ (R : Type u) [inst : CommRing R] [inst_1 : IsDedekindDomain R] (K : Type v) [inst_2 : Field K] [inst_3 : Algebra R K] [inst_4 : IsFractionRing R K], Set.univ.integer K = ⊤
If S is the whole set of places of K, then the S-integers are the whole of K.
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- Foundations
- Depth 162 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.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Top.topstatement and proof · cited by 9,680
- Fieldstatement and proof · cited by 7,404
- Set.univstatement and proof · cited by 3,945
- Subalgebrastatement · cited by 1,353
- IsFractionRingstatement and proof · cited by 738
- IsDedekindDomainstatement and proof · cited by 668
- IsDedekindDomain.HeightOneSpectrumstatement and proof · cited by 338
- Subalgebra.extproof · cited by 28
- Set.integerstatement and proof · cited by 8
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