Theorems · Theorem · number theory
NumberField.HeightOneSpectrum.one_lt_absNorm
∀ {R : Type u_2} [inst : CommRing R] [inst_1 : IsDedekindDomain R] (v : IsDedekindDomain.HeightOneSpectrum R)
[Module.Finite ℤ R] [inst_3 : Module.Free ℤ R], 1 < Ideal.absNorm v.asIdealThe norm of a maximal ideal is > 1
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 156 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- Idealstatement · cited by 4,748
- Module.Finitestatement and proof · cited by 1,032
- MonoidWithZeroHomstatement · cited by 704
- IsDedekindDomainstatement and proof · cited by 668
- Module.Freestatement and proof · cited by 597
- IsDedekindDomain.HeightOneSpectrumstatement and proof · cited by 338
- IsDedekindDomain.HeightOneSpectrum.asIdealstatement and proof · cited by 156
- Ideal.absNormstatement and proof · cited by 123
- Ideal.IsPrime.ne_topproof · cited by 82
- IsDedekindDomain.HeightOneSpectrum.ne_botproof · cited by 15
Cited by3
Results whose statement or proof uses this declaration.
- NumberField.HeightOneSpectrum.one_lt_absNorm_nnrealproof · cited by 8
- NumberField.RingOfIntegers.HeightOneSpectrum.one_lt_absNormproof · cited by 0