Theorems · Theorem · commutative algebra

Rat.valuation_le_one_iff_den

∀ {R : Type u_4} [inst : CommRing R] [inst_1 : IsDedekindDomain R] [inst_2 : Algebra R ℚ] [inst_3 : IsFractionRing R ℚ]
  {𝔭 : IsDedekindDomain.HeightOneSpectrum R} {x : ℚ},
  (IsDedekindDomain.HeightOneSpectrum.valuation ℚ 𝔭) x ≤ 1 ↔ ↑x.den ∉ 𝔭.asIdeal

Defined in: Mathlib.RingTheory.DedekindDomain.AdicValuation
Cited by: 0 results in Mathlib
Foundations: Depth 161 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing IsDedekindDomain Algebra IsFractionRing

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DFunLike.coestatement and proof · cited by 62,936
CommRingstatement and proof · cited by 17,173
Algebrastatement and proof · cited by 11,388
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Algebra.algebraMapproof · cited by 4,706
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Multiplicativestatement · cited by 875
Valuationstatement · cited by 823
IsFractionRingstatement and proof · cited by 738
IsDedekindDomainstatement and proof · cited by 668
WithZerostatement · cited by 586
Int.cast_natCastproof · cited by 393

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