Theorems · Theorem · commutative algebra

IsDedekindDomain.HeightOneSpectrum.exists_primeCompl_mul_eq_or_mul_eq

∀ {R : Type u_1} [inst : CommRing R] [IsDedekindDomain R] {K : Type u_2} [inst_2 : Field K] [inst_3 : Algebra R K]
  [IsFractionRing R K] (v : IsDedekindDomain.HeightOneSpectrum R) (x : K),
  ∃ n d, x * (algebraMap R K) ↑d = (algebraMap R K) n ∨ x * (algebraMap R K) n = (algebraMap R K) ↑d

All x : K can be written as n / d or d / n with n : R and d ∈ v.asIdealᶜ.

Defined in

Mathlib.RingTheory.DedekindDomain.AdicValuation

Cited by

1 results in Mathlib

Foundations

Depth 139 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingIsDedekindDomainFieldAlgebraIsFractionRing