Theorems · Theorem · number theory
IsDedekindDomain.selmerGroup.monotone
∀ {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] {S S' : Set (IsDedekindDomain.HeightOneSpectrum R)} {n : ℕ},
S ⊆ S' → IsDedekindDomain.selmerGroup ≤ IsDedekindDomain.selmerGroup- Cited by
- 0 results in Mathlib
- Foundations
- Depth 166 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Subgroupstatement · cited by 3,593
- Unitsstatement and proof · cited by 2,804
- HasQuotient.Quotientstatement and proof · cited by 2,301
- IsFractionRingstatement and proof · cited by 738
- IsDedekindDomainstatement and proof · cited by 668
- IsDedekindDomain.HeightOneSpectrumstatement and proof · cited by 338
- MonoidHom.rangestatement and proof · cited by 314
- powMonoidHomstatement and proof · cited by 35
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