Theorems · Theorem · number theory
NumberField.HeightOneSpectrum.one_lt_absNorm_nnreal
∀ {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.asIdeal)The norm of a maximal ideal as an element of ℝ≥0 is > 1
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 157 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- NNRealstatement · cited by 4,310
- Nat.cast_oneproof · cited by 2,501
- 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
Cited by9
Results whose statement or proof uses this declaration.
- NumberField.HeightOneSpectrum.adicAbvproof · cited by 21
- NumberField.HeightOneSpectrum.absNorm_ne_zeroproof · cited by 18
- NumberField.HeightOneSpectrum.isNonarchimedean_adicAbvproof · cited by 5
- NumberField.HeightOneSpectrum.embedding_mul_absNormproof · cited by 3
- NumberField.FinitePlace.norm_eq_one_iff_notMemproof · cited by 1
- NumberField.FinitePlace.norm_le_oneproof · cited by 1
- NumberField.FinitePlace.norm_lt_one_iff_memproof · cited by 1
- NumberField.RingOfIntegers.HeightOneSpectrum.one_lt_absNorm_nnrealproof · cited by 0