Theorems · Theorem · commutative algebra
IsDedekindDomain.HeightOneSpectrum.intValuation_singleton
∀ {R : Type u_1} [inst : CommRing R] [inst_1 : IsDedekindDomain R] (v : IsDedekindDomain.HeightOneSpectrum R) {r : R},
r ≠ 0 → v.asIdeal = Ideal.span {r} → v.intValuation r = WithZero.exp (-1)The I-adic valuation of a generator of I equals (-1 : ℤᵐ⁰)
- Cited by
- 3 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.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Idealstatement and proof · cited by 4,748
- Ideal.spanstatement and proof · 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.asIdealstatement and proof · cited by 156
- Associates.mkproof · cited by 137
Cited by3
Results whose statement or proof uses this declaration.
- IsDiscreteValuationRing.intValuation_maximalIdealproof · cited by 3
- Polynomial.valuation_X_eq_neg_oneproof · cited by 2
- PowerSeries.intValuation_Xproof · cited by 1