Theorems · Theorem · commutative algebra

IsDedekindDomain.HeightOneSpectrum.intValuation_zero_lt

∀ {R : Type u_1} [inst : CommRing R] [inst_1 : IsDedekindDomain R] (v : IsDedekindDomain.HeightOneSpectrum R)
  (x : ↥(nonZeroDivisors R)), 0 < v.intValuation ↑x

Nonzero divisors have valuation greater than zero.

Defined in: Mathlib.RingTheory.DedekindDomain.AdicValuation
Cited by: 0 results in Mathlib
Foundations: Depth 153 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing IsDedekindDomain

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DFunLike.coestatement and proof · cited by 62,936
CommRingstatement and proof · cited by 17,173
Submonoidstatement · cited by 3,086
Ideal.spanproof · cited by 948
nonZeroDivisorsstatement and proof · cited by 895
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
Multiplicative.ofAddproof · cited by 237
IsDedekindDomain.HeightOneSpectrum.asIdealproof · cited by 156

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