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Theorems · Theorem · commutative algebra

IsDedekindDomain.HeightOneSpectrum.ne_bot

∀ {R : Type u_1} [inst : CommRing R] (self : IsDedekindDomain.HeightOneSpectrum R), self.asIdeal ≠ ⊥
Defined in
Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas
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.

IsDedekindDomain.HeightOneSpectrum.prime · cited by 7HeightOneSpectrum.primeIsDedekindDomain.HeightOneSpectrum.intValuation_exists_uniformizer · cited by 3HeightOneSpectrum.intValu…NumberField.HeightOneSpectrum.one_lt_absNorm · cited by 3HeightOneSpectrum.one_lt_…FractionalIdeal.count_self · cited by 3FractionalIdeal.count_selfIsDedekindDomain.HeightOneSpectrum.intValuation_eq_exp_neg_multiplicity · cited by 2HeightOneSpectrum.intValu…PowerSeries.intValuation_eq_of_coe · cited by 2PowerSeries.intValuation_…FractionalIdeal.finprod_heightOneSpectrum_factorization · cited by 2FractionalIdeal.finprod_h…FractionalIdeal.count_maximal_coprime · cited by 2FractionalIdeal.count_max…Associates.finprod_ne_zero · cited by 2Associates.finprod_ne_zeroIsDedekindDomain.exists_sup_span_eq · cited by 2IsDedekindDomain.exists_s…Ideal.finprod_not_dvd · cited by 1Ideal.finprod_not_dvdIsDedekindDomain.HeightOneSpectrum.intValuation_liesOver · cited by 1HeightOneSpectrum.intValu…FractionalIdeal.count_finsuppProd · cited by 1FractionalIdeal.count_fin…Rat.HeightOneSpectrum.prime_natGenerator · cited by 1HeightOneSpectrum.prime_n…IsDedekindDomain.HeightOneSpectrum.uniformContinuous_algebraMap_liesOver · cited by 0HeightOneSpectrum.uniform…CommRing · cited by 17173CommRingIdeal · cited by 4748IdealBot.bot · cited by 4720Bot.botIsDedekindDomain.HeightOneSpectrum · cited by 338IsDedekindDomain.HeightOn…IsDedekindDomain.HeightOneSpectrum.asIdeal · cited by 156HeightOneSpectrum.asIdealHeightOneSpectrum.ne_botCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by15

Results whose statement or proof uses this declaration.