Theorems · Theorem · commutative algebra
IsDedekindDomain.HeightOneSpectrum.intValuation_ne_zero
∀ {R : Type u_1} [inst : CommRing R] [inst_1 : IsDedekindDomain R] (v : IsDedekindDomain.HeightOneSpectrum R) (x : R),
x ≠ 0 → v.intValuation x ≠ 0Nonzero elements have nonzero adic valuation.
- 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.
Cites10
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
- 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.intValuationstatement · cited by 53
- IsDedekindDomain.HeightOneSpectrum.intValuation_if_negproof · cited by 11
- WithZero.coe_ne_zeroproof · cited by 11
Cited by3
Results whose statement or proof uses this declaration.
- IsDedekindDomain.HeightOneSpectrum.intValuation_ne_zero'proof · cited by 4
- IsDiscreteValuationRing.exists_lift_of_le_oneproof · cited by 2
- IsDedekindDomain.HeightOneSpectrum.exists_intValuation_mul_sub_ltproof · cited by 1