Theorems · Theorem · commutative algebra
IsDedekindDomain.HeightOneSpectrum.intValuation_le_one
∀ {R : Type u_1} [inst : CommRing R] [inst_1 : IsDedekindDomain R] (v : IsDedekindDomain.HeightOneSpectrum R) (x : R),
v.intValuation x ≤ 1The v-adic valuation on R is bounded above by 1.
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 153 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.
Cites20
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
- map_zeroproof · cited by 1,614
- eq_or_neproof · cited by 1,117
- Ideal.spanproof · cited by 948
- Multiplicativestatement and proof · cited by 875
- Valuationstatement · cited by 823
- IsDedekindDomainstatement and proof · cited by 668
- WithZerostatement and proof · cited by 586
- IsDedekindDomain.HeightOneSpectrumstatement and proof · cited by 338
- IsDedekindDomain.HeightOneSpectrum.asIdealproof · cited by 156
- Associates.mkproof · cited by 137
Cited by9
Results whose statement or proof uses this declaration.
- IsDedekindDomain.HeightOneSpectrum.valuation_le_oneproof · cited by 9
- IsDedekindDomain.HeightOneSpectrum.intAdicAbv_le_oneproof · cited by 2
- IsDedekindDomain.HeightOneSpectrum.intValuation_eq_one_iffproof · cited by 1
- LaurentSeries.exists_Polynomial_intValuation_ltproof · cited by 1
- IsDedekindDomain.HeightOneSpectrum.valuation_of_unit_eqproof · cited by 1
- IsDedekindDomain.HeightOneSpectrum.exists_primeCompl_mul_eq_of_integerproof · cited by 1
- IsDedekindDomain.HeightOneSpectrum.Support.finiteproof · cited by 0
- IsDedekindDomain.HeightOneSpectrum.exists_valuation_sub_lt_of_integerproof · cited by 0