Theorems · Theorem · number theory
NumberField.RingOfIntegers.HeightOneSpectrum.one_lt_absNorm_nnreal
Deprecated since 2026-03-11Use NumberField.HeightOneSpectrum.one_lt_absNorm_nnreal instead.
∀ {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)Alias of NumberField.HeightOneSpectrum.one_lt_absNorm_nnreal.
The norm of a maximal ideal as an element of ℝ≥0 is > 1
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- Foundations
- Depth 158 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites12
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 · cited by 17,173
- Idealstatement · cited by 4,748
- NNRealstatement · cited by 4,310
- Module.Finitestatement · cited by 1,032
- MonoidWithZeroHomstatement · cited by 704
- IsDedekindDomainstatement · cited by 668
- Module.Freestatement · cited by 597
- IsDedekindDomain.HeightOneSpectrumstatement · cited by 338
- IsDedekindDomain.HeightOneSpectrum.asIdealstatement · cited by 156
- Ideal.absNormstatement · cited by 123
- NumberField.HeightOneSpectrum.one_lt_absNorm_nnrealproof · cited by 8
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