Theorems · Theorem · commutative algebra
IsDedekindDomain.HeightOneSpectrum.intAdicAbv_eq_one_iff
∀ {R : Type u_1} [inst : CommRing R] [inst_1 : IsDedekindDomain R] (v : IsDedekindDomain.HeightOneSpectrum R)
{b : NNReal} (hb : 1 < b) (r : R), (v.intAdicAbv hb) r = 1 ↔ r ∉ v.asIdeal- Cited by
- 1 results in Mathlib
- Foundations
- Depth 157 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingIsDedekindDomain
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
- Realstatement · cited by 25,697
- CommRingstatement and proof · cited by 17,173
- Idealstatement · cited by 4,748
- NNRealstatement and proof · cited by 4,310
- IsDedekindDomainstatement and proof · cited by 668
- AbsoluteValuestatement · cited by 363
- IsDedekindDomain.HeightOneSpectrumstatement and proof · cited by 338
- IsDedekindDomain.HeightOneSpectrum.asIdealstatement · cited by 156
- IsDedekindDomain.HeightOneSpectrum.intAdicAbvstatement and proof · cited by 11
- ne_iff_lt_iff_leproof · cited by 6
- IsDedekindDomain.HeightOneSpectrum.intAdicAbv_lt_one_iffproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- IsDedekindDomain.HeightOneSpectrum.adicAbv_coe_eq_one_iffproof · cited by 1