Theorems · Theorem · number theory
NumberField.FinitePlace.IsDedekindDomain.HeightOneSpectrum.embedding_mul_absNorm
Deprecated since 2026-03-11Use NumberField.HeightOneSpectrum.embedding_mul_absNorm instead.
∀ (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},
x ≠ 0 →
‖(NumberField.FinitePlace.embedding v) ((algebraMap R K) x)‖ *
↑(Ideal.absNorm (v.maxPowDividing (Ideal.span {x}))) =
1Alias of NumberField.HeightOneSpectrum.embedding_mul_absNorm.
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 190 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement · cited by 53,352
- Realstatement · cited by 25,697
- CommRingstatement · cited by 17,173
- Algebrastatement · cited by 11,388
- RingHomstatement · cited by 10,189
- Fieldstatement · cited by 7,404
- Norm.normstatement · cited by 5,413
- Idealstatement · cited by 4,748
- Algebra.algebraMapstatement · cited by 4,706
- Module.Finitestatement · cited by 1,032
- Ideal.spanstatement · cited by 948
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.