Theorems · Theorem · number theory
NumberField.HeightOneSpectrum.absNorm_ne_zero
∀ {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], ↑(Ideal.absNorm v.asIdeal) ≠ 0The norm of a maximal ideal as an element of ℝ≥0 is ≠ 0
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 158 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 · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Idealstatement · cited by 4,748
- NNRealstatement · cited by 4,310
- 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 · cited by 156
- Ideal.absNormstatement · cited by 123
- ne_zero_of_ltproof · cited by 17
Cited by18
Results whose statement or proof uses this declaration.
- NumberField.FinitePlace.norm_embeddingproof · cited by 6
- NumberField.HeightOneSpectrum.adicAbv_defstatement · cited by 4
- NumberField.HeightOneSpectrum.embedding_mul_absNormproof · cited by 3
- NumberField.HeightOneSpectrum.rankOne_hom'_defstatement · cited by 2
- NumberField.HeightOneSpectrum.toNNReal_valued_eq_adicAbvstatement · cited by 2
- NumberField.FinitePlace.norm_defstatement and proof · cited by 1
- NumberField.FinitePlace.norm_embedding'statement and proof · cited by 1
- NumberField.FinitePlace.norm_embedding_intstatement and proof · cited by 1
- NumberField.rankOne_hom'_defstatement · cited by 0
- NumberField.FinitePlace.norm_def'statement · cited by 0
- NumberField.FinitePlace.norm_def_intstatement · cited by 0
- NumberField.toNNReal_valued_eq_adicAbvstatement · cited by 0