Theorems · Theorem · commutative algebra

IsDedekindDomain.HeightOneSpectrum.intValuation_eq_one_iff_mem_primeCompl

∀ {R : Type u_1} [inst : CommRing R] [inst_1 : IsDedekindDomain R] (v : IsDedekindDomain.HeightOneSpectrum R) (r : R),
  v.intValuation r = 1 ↔ r ∈ v.asIdeal.primeCompl

The v-adic valuation of r : R is equal to 1 if and only if r ∈ vᶜ.

Defined in

Mathlib.RingTheory.DedekindDomain.AdicValuation

Cited by

2 results in Mathlib

Foundations

Depth 156 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingIsDedekindDomain