Theorems · Theorem · commutative algebra
IsDedekindDomain.HeightOneSpectrum.exists_valuation_sub_lt_of_integer
∀ {R : Type u_1} [inst : CommRing R] [inst_1 : IsDedekindDomain R] {K : Type u_2} [inst_2 : Field K]
[inst_3 : Algebra R K] [inst_4 : IsFractionRing R K] (v : IsDedekindDomain.HeightOneSpectrum R) {x : K},
(IsDedekindDomain.HeightOneSpectrum.valuation K v) x ≤ 1 →
∀ (γ : (WithZero (Multiplicative ℤ))ˣ),
∃ a, (IsDedekindDomain.HeightOneSpectrum.valuation K v) ((algebraMap R K) a - x) < ↑γGiven x ∈ 𝒪[K] we can find a : A such that a is close to x by the valuation v.
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- Foundations
- Depth 161 from the axioms · uses propext, Classical.choice, Quot.sound
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