Theorems · Theorem · number theory
IsDedekindDomain.FiniteAdeleRing.infinite_valued_ne_one_of_not_isUnit
∀ {R : Type u_1} [inst : CommRing R] [inst_1 : IsDedekindDomain R] {K : Type u_2} [inst_2 : Field K]
[inst_3 : Algebra R K] [inst_4 : IsFractionRing R K] {a : IsDedekindDomain.FiniteAdeleRing R K},
(∀ (v : IsDedekindDomain.HeightOneSpectrum R), a v ≠ 0) → ¬IsUnit a → {v | Valued.v (a v) ≠ 1}.Infinite- Cited by
- 0 results in Mathlib
- Foundations
- Depth 193 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Set.ofPredstatement and proof · cited by 6,101
- Set.Finiteproof · cited by 1,814
- IsUnitstatement and proof · cited by 1,602
- Multiplicativestatement · cited by 875
- Valuationstatement · cited by 823
- IsFractionRingstatement and proof · cited by 738
- IsDedekindDomainstatement and proof · cited by 668
- WithZerostatement · cited by 586
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.