Theorems · Theorem · commutative algebra
IsDedekindDomain.HeightOneSpectrum.ne_bot
∀ {R : Type u_1} [inst : CommRing R] (self : IsDedekindDomain.HeightOneSpectrum R), self.asIdeal ≠ ⊥- Cited by
- 15 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Idealstatement · cited by 4,748
- Bot.botstatement · cited by 4,720
- IsDedekindDomain.HeightOneSpectrumstatement and proof · cited by 338
- IsDedekindDomain.HeightOneSpectrum.asIdealstatement · cited by 156
Cited by15
Results whose statement or proof uses this declaration.
- IsDedekindDomain.HeightOneSpectrum.primeproof · cited by 7
- IsDedekindDomain.HeightOneSpectrum.intValuation_exists_uniformizerproof · cited by 3
- NumberField.HeightOneSpectrum.one_lt_absNormproof · cited by 3
- FractionalIdeal.count_selfproof · cited by 3
- IsDedekindDomain.HeightOneSpectrum.intValuation_eq_exp_neg_multiplicityproof · cited by 2
- PowerSeries.intValuation_eq_of_coeproof · cited by 2
- FractionalIdeal.finprod_heightOneSpectrum_factorizationproof · cited by 2
- FractionalIdeal.count_maximal_coprimeproof · cited by 2
- Associates.finprod_ne_zeroproof · cited by 2
- IsDedekindDomain.exists_sup_span_eqproof · cited by 2
- Ideal.finprod_not_dvdproof · cited by 1
- IsDedekindDomain.HeightOneSpectrum.intValuation_liesOverproof · cited by 1