Theorems · Theorem · number theory
NumberField.FinitePlace.norm_eq_one_iff_notMem
∀ (K : Type u_1) [inst : Field K] {R : Type u_2} [inst_1 : CommRing R] [inst_2 : Algebra R K]
[inst_3 : IsDedekindDomain R] [inst_4 : IsFractionRing R K] (v : IsDedekindDomain.HeightOneSpectrum R)
[inst_5 : Module.Finite ℤ R] [inst_6 : Module.Free ℤ R] (x : R),
‖(NumberField.FinitePlace.embedding v) ((algebraMap R K) x)‖ = 1 ↔ x ∉ v.asIdealThe v-adic norm of an integer is 1 if and only if it is not in the ideal.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 189 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
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
- Realstatement and proof · cited by 25,697
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Norm.normstatement · cited by 5,413
- Idealstatement · cited by 4,748
- Algebra.algebraMapstatement and proof · cited by 4,706
- Module.Finitestatement and proof · cited by 1,032
- IsFractionRingstatement and proof · cited by 738
- IsDedekindDomainstatement and proof · cited by 668
Cited by1
Results whose statement or proof uses this declaration.
- NumberField.FinitePlace.mk_eq_iffproof · cited by 1